Engtrig Reviewer

ENGTRIG REVIEWER (Page 1 of 23)

QUESTION #1:The measure of an angle whose vertex is at the center of a circle which cuts an arc on

the circle equal in length to the radius of the circle is a/an ________.

ANSWER: radian

QUESTION #2:One half of the difference between the largest possible value of the function and the

smallest possible value is a/an ________.

ANSWER: amplitude

QUESTION #3:The measure of 2.25 revolutions counter-clockwise is ________ degrees.

ANSWER: 810

QUESTION #4:Simplify: cos(90°) + 3sin(270°)

ANSWER: 3

QUESTION #5:Simplify: tan(0°) – 6sin(90°)

ANSWER: -6

QUESTION #6:Simplify: 4csc(270°) + 3sec(180°) – 5tan(360°)

ANSWER: -7

QUESTION #7:The horizontal distance from point at which the curve repeats is a/an ________.

ANSWER: period

QUESTION #8:A runner finds that after running around a circular track thrice is equivalent to running a

distance of 6 km. What is the radius of the circular track?

ANSWER: (1/π) km

QUESTION #9:An angle is considered negative if the rotation is ________.

ANSWER: clockwise


QUESTION #10:The functions of tangent and cotangent have ________ period.

ANSWER: π/k

QUESTION #11:220° is equal to ________ radians.

ANSWER: 11π/9

QUESTION #12:The angle is said to be in ________ if it is drawn in the xy-plane with its vertex at the

origin and its initial side on the positive x-axis.

ANSWER: standard position

QUESTION #13:The trigonometric functions that have positive values in Quadrant III are ________.

ANSWER: tangent and cotangent

QUESTION #14:________ is the rate at which the central angle, θ, is changing.

ANSWER: Angular speed

QUESTION #15:A saw blade having a blade of 6-in radius spins at 50π ft/s. What is its angular speed?

ANSWER: 100π rad/s

QUESTION #16:The vertical asymptote of the trigonometric function: f(x) = tan(x + π/4) between 0 to 2π

is ________.

ANSWER: 5π/4

QUESTION #17:The coterminal angle of 13π/3 between 0 to 2π are ________.

ANSWER: π/3

QUESTION #18:The reference angle of 2π/3 is ________.

ANSWER: π/3


QUESTION #19:The coterminal angle to the negative angle -128°, θ, where 0° < θ < 360° is ________.

ANSWER: 232°

QUESTION #20:The measure of the reference angle for -1275°, φ, where 0° < φ < 90° is ________.

ANSWER: 15°

QUESTION #21:If the point (4,3) lies on the terminal side of the angle, θ, then sin θ = ________.

ANSWER: 3/5

QUESTION #22:A roller with 10-in radius makes 90 revolutions per minute. Determine the angular

speed of the roller in radians per second.

ANSWER: 3π rad/s

QUESTION #23:A wheel of diameter 2 m rotates an angular speed of 240 rad/min. What is the linear

speed of a point on the outer rim of the wheel?

ANSWER: 8 m/s

QUESTION #24:The compliment of θ = 33° 46' 24'' is ________.

ANSWER: 56° 13' 36''

QUESTION #25:The graph of y = sin x is symmetrical with respect to the ________.

ANSWER: origin

QUESTION #26:A certain angle in a circle of radius 5m is subtended by an arc of length 6m. What is the

measure of the angle in radians?

ANSWER: 1.2


QUESTION #27:Point P (1,2) lies on the terminal side of angle A in the standard position. Determine

cos(A).

ANSWER: √55

QUESTION #28:Given triangle ABC, csc B = 17/15 and a = 3. Determine the length of the hypotenuse.

ANSWER: 51/8

QUESTION #29:Given sin(48°) = 3/4, what is csc(42°)?

ANSWER: 4√77

QUESTION #30:Evaluate sec(17π/3)

ANSWER: 2

QUESTION #31:Evaluate sin(240°)

ANSWER: 2√33

QUESTION #32:Evaluate tan(-13π/2)

ANSWER: undefined

QUESTION #33:Evaluate tan(30°)

ANSWER: √33

QUESTION #34:Evaluate sin(38π/4)

ANSWER: -1


QUESTION #35:If cos(56°) = 5/13, what is sec(34°)?

ANSWER: 13/12

QUESTION #36:Point A(3,-5) lies on the terminal side of angle B in the standard position. What is the

value of sinB?

ANSWER: −5√3434

QUESTION #37:Express sin(A – 90°) as a trigonometric function of A.

ANSWER: - cos A

QUESTION #38:Express tan(5π + A) as a trigonometric function of A.

ANSWER: tan A

QUESTION #39:Express csc(A + 9π/2) as a trigonometric function of A.

ANSWER: sec A

QUESTION #40:Express sin(A – 5π/2) as a trigonometric function of A.

ANSWER: - cos A

QUESTION #41:Express sec(180° + A) as a trigonometric function of A.

ANSWER: - sec A

QUESTION #42:Express tan(720° – A) as a trigonometric function of A.

ANSWER: - tan A


QUESTION #43:If sinA = 3/7 and secA > 0, determine the value of the other trigonometric ratios.

ANSWER: cosA = 2√107

, tanA = 3√1020

cscA = 73 , secA = 7√1020

, cotA = 2√103

QUESTION #44:If secθ = 4/3 and sinθ < 0, determine the value of the other trigonometric ratios.

ANSWER: sinθ = −√74

, cosθ = 34 , tanθ = −√7

3

cscθ = − 4√77

, cotθ = −3√77

QUESTION #45:If tan t = -2 and csc t > 0, determine the value of the other trigonometric ratios.

ANSWER: sin t = 2√55

, cos t = −√55

csc t = √52

, sec t = −√5 , cot t = −12

QUESTION #46:

If cot B = √23

, csc B < 0, determine the value of the other trigonometric ratios.

ANSWER: sin B = −3√1111

, cos B = −√2211

, tan B = 3√22

csc B = −√113

, sec B = −√222

QUESTION #47:

If secθ = 4√69

and tanθ < 0, determine the value of the other trigonometric ratios.

ANSWER: sinθ = −√108

, cosθ = 3√68

, tanθ = −√159

cscθ = − 4√105

, cot = −3√155


QUESTION #48:

Evaluate sec(1200o)+sin(−225o)−3csc(330o)

2 tan( 7π4

)−cot(135o)+cos (−9π)

ANSWER: 8+√24

QUESTION #49:

Evaluate 4 tan(5π4 )cos (600o)+sin3(−1020o)cot(−29π6 )+sec(−5π)csc(690o)

tan (2π)cos(300o)−√3sin(11π2 )sec2(855o)ANSWER: 3√3

16

QUESTION #50:

Evaluate cos( 7π

3)2

+tan(1125o)2+sin (780o)2

sin( π2 )csc(−450)+2sec(18π)

ANSWER: 0

QUESTION #51:

Express cos(990o+θ)cot(θ−7π)csc (−450o−θ)

sin (540o+θ) tan(−7π2

+θ)as a trigonometric function of θ

ANSWER: -sec(θ)

QUESTION #52:The amplitude of the curve y = 3 + 2cos(3x – π) is ________.

ANSWER: 2

QUESTION #53:The period of the curve y = 3 + 2cos(3x – π) is ________.

ANSWER: 2π3


QUESTION #54:The phase shift of the curve y = 3 + 2cos(3x – π) is ________.

ANSWER: π3 units to the right

QUESTION #55:The vertical shift of the curve y = 3 + 2cos(3x – π) is ________.

ANSWER: 3 units upward

QUESTION #56:

The amplitude of the curve y=3sin(12x+π

6)−3 is ________.

ANSWER: 3

QUESTION #57:

The period of the curve y=3sin(12x+π

6)−3 is ________.

ANSWER: 4π

QUESTION #58:

The phase shift of the curve y=3sin(12x+π

6)−3 is ________.

ANSWER: π3 units to the left

QUESTION #59:

The vertical shift of the curve y=3sin(12x+π

6)−3 is ________.

ANSWER: 3 units downward

QUESTION #60:The amplitude of the curve y=3sin(4x−

π2)+1 is ________.

ANSWER: 3

QUESTION #61:The period of the curve y=3sin(4x−

π2)+1 is ________.

ANSWER: π/2


QUESTION #62:The phase shift of the curve y=3sin(4x−

π2)+1 is ________.

ANSWER: π8 units to the right

QUESTION #63:The vertical shift of the curve y=3sin(4x−

π2)+1 is ________.

ANSWER: 1 unit upward

QUESTION #64:A backpacker notes that from a certain point on level ground, the angle of elevation to

a point at the top of a tree is 30°. After walking 30 meters closer to the tree, the backpacker notes the angle of elevation is 45°. Determine the height of the tree.

ANSWER: 15√3+15meters

QUESTION #65:The Golden Gate Bridge has two main towers of equal height that support two main

cables. A visitor on a tour boat passing through the San Francisco Bay views the top of one of the towers and estimates the angle of elevation to be 30°. After sailing 670 feet closer, he estimates the angle of elevation to this same tower to be 60°. Approximate the height of the tower.

ANSWER: 335√3 feet

QUESTION #66:An electric-powered toy truck is moving at 10 miles per hour. If each of its wheels has a

diameter of 1 foot, how fast are they turning in rpm?

ANSWER: 880/π rpm

QUESTION #67:A person looks to the top of a tower at an angle of elevation of 30°. After walking 10 ft

toward the base of the tower, the angle of elevation becomes 45°. How much farther must the person walk toward the base of the tower so that the angle of elevation becomes 60°?

ANSWER: 10 √33

ft


QUESTION #68:At 1:00pm, Elaine saw her friend Angel waving at her from the top of a building, and

she measures the angle of elevation to be 30°. At this point, she starts walking at a constant speed towards the entrance of the building. At 1:05pm, Elaine stopped walking and looked up to measure that the angle of elevation has become 45°. If the building is 300 ft tall, how fast was Elaine walking?

ANSWER: √3−1 fts

QUESTION #69:At 1:00pm, Elaine saw her friend Angel waving at her from the top of a building, and

she measures the angle of elevation to be 30°. At this point, she starts walking at a constant speed towards the entrance of the building. At 1:05pm, Elaine stopped walking and looked up to measure that the angle of elevation has become 45°. if Elaine was walking at 1 ft/s, how tall is the building?

ANSWER: 150√3+150 feet

QUESTION #70:Express sin(90°-θ) – tanθcos(90°-θ) as a trigonometric function of θ

ANSWER: secθ

QUESTION #71:Evaluate –cos(83°)cos(38°) – sin(83°)sin(38°)

ANSWER: −√22

QUESTION #72:Evaluate sec(15°) + csc(15°) + cot(15°)

ANSWER: 2+√3+2√6

QUESTION #73:Evaluate cos(157.5°)

ANSWER: −√2+√22


QUESTION #74:

Evaluate sin(140o)+sin(20o)

cos(140o)−cos(20o)

ANSWER: −√33

QUESTION #75:

Evaluate sin(5π24

)cos( 25π24

)

ANSWER: −1+√22

QUESTION #76:The cofunction identity of sec(u) is ________.

ANSWER: csc(π2−u)

QUESTION #77:The inverse sine function has a domain of ________.

ANSWER: [-1, 1]

QUESTION #78:The expression 2sin(x)cos(x) is equivalent to the double angle identity ________.

ANSWER: sin(2x)

QUESTION #79:The value of cos-1(0) is ________.

ANSWER: (2N+1)(π/2) where N is any integer

QUESTION #80:The expression cos(s)cos(t) – sin(s)sin(t) is equivalent to ________.

ANSWER: cos(s+t)

QUESTION #81:These identities allow us to find the values of trigonometric function at 2x from the

values of x.

ANSWER: double-angle identities


QUESTION #82:

The expression tan(s)−tan (t)1+tan (s) tan( t) is equivalent to ________.

ANSWER: tan(s – t)

QUESTION #83:If sec(A) = - 3/4 and tan(B) = - 8/15 for a quadrant III angle A and quadrant II angle B,

in what quadrant does A+B reside?

ANSWER: quadrant I

QUESTION #84:The solution in the interval [0,2π) of the equation cos(θ/2) – 1 = 0 is ________.

ANSWER: 0

QUESTION #85:

Evaluate cos[arcsin ( √22 )+arccos( 35)]

ANSWER: −√210

QUESTION #86:Evaluate sin(112.5o)+cos(arctan(2))

ANSWER: √2+√22

+√55

QUESTION #87:Given that sec(A) = 4/3, sin(A) < 0, sin(B) = 3/5, B is in quadrant II, evaluate tan(A-B).

ANSWER: 64−25√727

QUESTION #88:

Given that sec(A) = 4/3, sin(A) < 0, sin(B) = 3/5, B is in quadrant II, evaluate 1+cot Bsin A

ANSWER: 21+16√721


QUESTION #89:If csc(A) = -17/15, tan(B) = 3/4, A is in quadrant IV, B is in quadrant III, evaluate

sin(A+B).

ANSWER: 36/85


cos(A+2B).

ANSWER: 416/425


tan((A/2)+B).

ANSWER: 111/73

QUESTION #92:If csc(A) = -17/15, tan(B) = 3/4, A is in quadrant IV, B is in quadrant III, determine the

location of angle (A+B).

ANSWER: Quadrant II

QUESTION #93:If sin(A) = 2/3, sin(B) = 1/3 and A and B are between 0 and π/2, evaluate sin(A+B).

ANSWER: 4√2+√59

QUESTION #94:Evaluate tan[arccos(-4/5)]

ANSWER: -3/4

QUESTION #95:

Evaluate sin(2arcsin ( 35 )+12 arccos( 149 ))ANSWER: 120+14√6

175

QUESTION #96:Evaluate arccos(cos((19π)/6))

ANSWER: (7π)/6


QUESTION #97:Evaluate sin(arccos(-5/6) – arctan(-2))

ANSWER: √55−10√530

QUESTION #98:

Evaluate tan(2arcsin (−√32

))ANSWER: √3

QUESTION #99:

Evaluate sin(arcsin ( 45 )−arcsec( 32))

ANSWER: 8−3√515

QUESTION #100:With the interval of 0° ≤ x < 360°, determine all solutions of the equation

3 tan 3x+3sec 2x – tan x – 4=0

ANSWER: {x|x = 30°, 135°, 150°, 210°, 315°, 330°}


2cos x+2sin x=√6

ANSWER: {x|x = 15°, 75°}


tan xcot x+√3 tan x−√3cot x−3=0

ANSWER: {x|x = 60°, 150°, 240°, 330°}

QUESTION #103:The ________ often applies for cases when one side and two angles of an oblique

triangle or two sides and the angle opposite one of those sides of an oblique triangle are known.

ANSWER: sine law


QUESTION #104:The ________ often applies for cases when two sides and an included angle of an

oblique triangle or three sides of an oblique triangle are known.

ANSWER: cosine law

QUESTION #105:Determine angle B in triangle ABC if a = 16, b = 20 and c = 32.

ANSWER: 125.10°

QUESTION #106:In triangle XYZ, x = 23.5, y = 9.8 and X = 39.7°. How many possible triangles can be

formed from the given parts?

ANSWER: 1

QUESTION #107:The argument, θ, of the complex number 2 – 2i is ________.

ANSWER: 315°

QUESTION #108:The rectangular coordinates of (10, π/3) is ________.

ANSWER: (5,5√3)

QUESTION #109: Determine the cubic roots of i.

ANSWER: −i , √32

+ 12i ,−√3

2+12i

QUESTION #110:(1+i)6 in polar form is equal to ________.

ANSWER: 8cis( 3π2 )

QUESTION #111:Simplify (-3+2i)2 in rectangular form.

ANSWER: 5 – 12i


QUESTION #112:The equation r = 2secθ is equal to ________ in rectangular coordinates.

ANSWER: x = 2

QUESTION #113:The polar form of the complex number -4i is ________.

ANSWER: 4cis(270°)

QUESTION #114:The rectangular form of the complex number 3cis(180°) is ________.

ANSWER: -3

QUESTION #115:What are the polar coordinates of point P (−1,√3) ?

ANSWER: (2, 120°)

QUESTION #116:If the polar coordinates of point P are (√2 ,315o) , determine the rectangular

coordinates of point P.

ANSWER: (1, -1)

QUESTION #117:The product of [8cis(210°)][(1/2)cis(160°)]

ANSWER: 4cis(10°)

QUESTION #118:In triangle ABC, if a = 32, c = 13 and C = 26°, how many triangles are formed?

ANSWER: none

QUESTION #119:In triangle ABC, a = 24, b = 61 and c = 38. What is the area of the triangle ABC?

ANSWER: 164.62 square units

QUESTION #120:In triangle ABC, a = 24, b = 61 and c = 38. What is the measure of angle B?

ANSWER: 158.84°


QUESTION #121:In triangle ABC, if A = 38°, b = 89 and c = 139, what is the altitude of the triangle

measured from vertex C to side c?

ANSWER: 54.79

QUESTION #122:In triangle ABC, if a = 12, A = 105° and B = 44°, determine b.

ANSWER: 8.63

QUESTION #123:Convert the equation x2 + y2 – 5x + 6y = 0 into polar form.

ANSWER: r2 – 5rcosθ + 6rsinθ = 0

QUESTION #124:

Convert r=43sin 2θ into rectangular form.

ANSWER: xy

(x2+ y2)32

=38

QUESTION #125:Observers at A and B are 362 ft apart and looking at point C. How far is C from each

observer if angle CBA = 37.33° and angle CAB = 68.50°?

ANSWER: Observer A is 228.17 ft away from point C while observer B is 350.09 ft away from point C.

QUESTION #126:Determine the remaining parts of triangle ABC given C = 27.03°, a = 4174 and c =

2033.

ANSWER: (Two possible answers) A1 = 68.92°, B1 = 84.05°, b1 = 4449.37, A2 = 111.08°, B2=41.89°, b2 = 2986.95

QUESTION #127:Determine the remaining parts of triangle ABC given A = 23.63°, a = 22.7 and b = 30.4.

ANSWER: (Two possible answers) A1 = 32.47°, C1 = 123.90°, c1 = 47.01, A2 = 147.53°, C2 = 8.84°, c2 = 8.70


QUESTION #128:Determine the remaining parts of triangle ABC given b = 15, c = 20 and B = 29°.

ANSWER: (Two possible answers) A1 = 40.27°, C1 = 110.73°, c1 = 28.94, A2 = 139.73°, C2 = 11.27°, c2 = 6.05

QUESTION #129:Determine the remaining parts of triangle ABC given a = 4.56, A = 43° and B = 57°.

ANSWER: C = 80°, c = 6.58 and b = 5.61

QUESTION #130:Two forces of 528 lb and 603 lb are acting at the same point and make an angle of

67.78° with one another. Determine the magnitude of the resultant and the angle the resultant makes with the smaller force.

ANSWER: The magnitude of the resultant is 633.71 lb and the angle the resultant makes with the smaller force is 50.47°.

QUESTION #131:Three circles of radii 3, 4 and 5 touch each other externally. Determine the angle of the

triangle formed by joining their centers.

ANSWER: 73.40°, 48.19°, 58.41°

QUESTION #132:A pole leans away from the sun at an angle of 7° from the vertical. When the angle of

elevation of the sun is 51°, the pole casts a shadow of 47 ft long on level ground. How long is the pole?

ANSWER: The length of the pole is 50.78 ft.

QUESTION #133:A waterfall is 8 km northeast (N 45° E) of a mountain. A valley is 4 km from the

waterfall and has a bearing of S 30° E from the waterfall. What is the bearing and distance from the valley to the mountain.

ANSWER: The distance from the valley to the mountain is 7.965 km and the bearing from the valley to the mountain is S 75.03° W

QUESTION #134:Two ships leave port at 3:00 pm. Ship A is headed at a bearing of N 35° W and is

traveling at 12 miles per hour while ship B is traveling 13.5 miles per hour at a bearing of S 47° W. How far apart are the ships at 6:00 pm?

ANSWER: Ship A is 57.81 miles apart from Ship B


QUESTION #135:Two ships leave port at 3:00 pm. Ship A is headed at a bearing of N 35° W and is

traveling at 12 miles per hour while ship B is traveling 13.5 miles per hour at a bearing of S 47° W. At 6:00pm, what is the bearing from ship A to ship B?

ANSWER: Ship A has a bearing of S 8.92° W to ship B.

QUESTION #136:

Simplify (−4−3 i)5(2cis73.32o)3

(4cis305.40)4(−1+√3)6into polar form

ANSWER: 634.53cis(82.71°)

QUESTION #137:Determine the solution to the equation z5 + 3 = 3i in rectangular form.

ANSWER: 1.1896+0.6061i, -0.2088+1.3187i, -1.3187+0.2088i, -0.6061-1.1896i, 0.9441-0.9441i

QUESTION #138:A number of the form a + bi is a/an ________.

ANSWER: complex number

QUESTION #139:In a number of the form a + bi, if a = 0, the number become a/an ________.

ANSWER: imaginary number

QUESTION #140:In a number of the form a + bi, if b = 0, the number become a/an ________.

ANSWER: real number

QUESTION #141:A/an ________ is a part of the surface of a sphere bounded by three arcs of great

circles.

ANSWER: spherical triangle

QUESTION #142:A/an ________ is a spherical triangle having a side equal to 90°.

ANSWER: quadrantal triangle


QUESTION #143:A/an ________ is a spherical triangle having two equal sides.

ANSWER: isosceles triangle

QUESTION #144:The amount by which the sum of the angles of a spherical triangle exceeds 180° is

called ________.

ANSWER: spherical excess

QUESTION #145:A/an ________ is formed when a plane passes through the center of the sphere.

ANSWER: great circle

QUESTION #146:The first Napier's rule states that the sine of any middle part is equal to the product of

the ________ of the adjacent parts.

ANSWER: tangent

QUESTION #147:The second Napier's rule states that the sine of any middle part is equal to the product

of the ________ of the opposite parts.

ANSWER: cosine

QUESTION #148:If the angles A, B, C of a spherical triangle are 75°, 92° and 85° respectively, determine

side a of the polar triangle.

ANSWER: 75.11°


side b of the polar triangle.

ANSWER: 90.73°


side c of the polar triangle.

ANSWER: 85.36°


QUESTION #151:Convert the polar equation secθ = 2 into rectangular form.

ANSWER: x=2√x2+y2

QUESTION #152:Convert the equation xy = 1 into polar form.

ANSWER: r2sinθcosθ = 1

QUESTION #153:

Convert point P( √3 ,−5π3 ) into rectangular coordinates.

ANSWER: ( √32, 32

)

QUESTION #154:Convert point P( −√6 ,−√2 ) into polar coordinates.

ANSWER: ( 2√2 , π6 )

QUESTION #155:

Simplify 5cis (45o)−3cis (225o)

4 cis(270o)into polar form.

ANSWER: 2cis(135°)

QUESTION #156:Simplify [√2cis(315o)−10 cis(−60o)][10 cis(90o)] into rectangular form.

ANSWER: -76.60 – 40i

QUESTION #157:

Simplify [ 1−√3 i2 ]

6

into rectangular form.

ANSWER: 1

QUESTION #158:Determine the remaining parts of the spherical triangle ABC given B = 90°, a = 59° 30'

and c = 99° 40'.

ANSWER: b = 94° 53' 20'', A = 59° 51' 25.5'', C = 98° 20' 57.87''


QUESTION #159:Determine the remaining parts of the spherical triangle ABC given B = 90°, b= 73° 20'

and c = 99° 40'.

ANSWER: no solution

QUESTION #160:Determine the remaining parts of the spherical triangle ABC given B = 90°, a = 59° 30'

and b = 73° 20'.

ANSWER: c = 55° 35' 30'', A = 64° 4' 52.17'', C = 59° 27' 10.32''

QUESTION #161:Determine the remaining parts of the spherical triangle ABC given C = 90°, a = 47° 10'

20'' and b = 74° 50' 35''.

ANSWER: c = 79° 45' 42.16'', A = 48° 10' 55.4'', B = 78° 45' 48.33''

QUESTION #162:Determine the remaining parts of the spherical triangle ABC given C = 90°, b = 21° 30'

5'' and B = 58° 10' 15''.

ANSWER: (Two possible answers) a1 = 14° 9' 14.6'', A1 = 34° 31' 47.38'', c1 = 25° 33' 22.07'', a2 = 165° 50' 45.4'', A2 = 145° 28' 12.62'', c2 = 154° 26' 37.93''

QUESTION #163:Determine the remaining parts of the spherical triangle ABC given B = 90°, C = 82° 39'

and a = 70° 23'.

ANSWER: A = 70° 33' 3.75'', b = 87° 23' 21.7'', c = 82° 12' 9.12''

QUESTION #164:Determine the remaining parts of the spherical triangle ABC given B = 90°, A = 126°

and a = 130°.

ANSWER: (Two possible answers) b1 = 71.24°, c1 = 59.98°, C1 = 66.13°, b2 = 108.76°, c2 = 120.02°, C2 = 113.87°

QUESTION #165:Determine the remaining parts of the spherical triangle ABC given a = 67° 19' 30'', b =

52° 18' 20'' and c = 37° 13' 50''

ANSWER: A = 102° 13' 13.66'', B = 56° 56' 37.38'', C = 39° 51' 18.19''


QUESTION #166:Determine the remaining parts of the spherical triangle ABC given A = 106° 42', B = 37°

28' and c = 49° 40'.

ANSWER: C = 52° 45' 27.91'', a = 66° 30' 54.34'', b = 35° 37' 30.29''

QUESTION #167:Determine the remaining parts of the spherical triangle ABC given A = 126°, b = 62° 42'

and c = 102°.

ANSWER: a = 65° 26' 47.2'', B = 52° 13' 14.98'', C = 119° 32' 24.61''

QUESTION #168:Determine the remaining parts of the spherical triangle ABC given A = 143° 54', B =

104° 08' and C = 86° 12'

ANSWER: a = 148° 24' 17.57'', b = 120° 25' 33.62'', c = 62° 31' 44.63''

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