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Sine (sin) =
?
?
hypotenuse
oppositeSine (sin) =
Cosine (cos) =
?
?
hypotenuse
adjacentCosine (cos) =
Tangent (tan) =
?
?
adjacent
oppositeTangent (tan) =
sin D= ?
?
sin𝐷 =𝐴𝐵
𝐴𝐷
cos D= ?
?
cos𝐷 =𝐷𝐵
𝐴𝐷
tan D= ?
?
tan𝐷 =𝐴𝐵
𝐷𝐵
sin A=
C
B
A
5
12
13
?
?
sin A=
C
B
A
5
12
13
13
5
(opposite)
(hypotenuse)
(opposite)
(hypotenuse)
sin B=
C
B
A
5
12
13
?
?
sin B=
C
B
A
5
12
13
13
12
(hypotenuse)
(opposite)
(hypotenuse)
(opposite)
cos B=
C
B
A
5
12
13
?
?
cos B=
C
B
A
5
12
13
13
5 (adjacent)
(hypotenuse)
(adjacent)
(hypotenuse)
tan A=
C
B
A
5
12
13
?
?
tan A=
C
B
A
5
12
13
12
5
(adjacent)
(opposite)
(opposite)
(adjacent)
If the sin𝑂 =3
5for ∆𝑀𝑂𝑁 with
right ∠𝑀, what is the cos𝑁?
If the sin𝑂 =3
5for ∆𝑀𝑂𝑁 with
right ∠𝑀, what is the cos𝑁?
MO
N
sin𝑂 =3
5=
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒(hypotenuse)
3
(opposite)5 cos𝑁 =
3
5=
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒(adjacent)
If the cos 𝐴 =12
13for ∆𝑀𝐴𝐷 with
right ∠𝑀, what is the sin𝐷?
If the cos 𝐴 =12
13for ∆𝑀𝐴𝐷 with
right ∠𝑀, what is the sin𝐷?
cos 𝐴 =12
13=
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
(hypotenuse)
12
(opposite)13 sin𝐷 =
12
13=
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒(adjacent)
MD
A
Which trigonometric expression has the same
value as sin 48°?
Which trigonometric expression has the same
value as sin 48°?
cos 42°
Which trigonometric expression has the same
value as cos 52°?
Which trigonometric expression has the same
value as cos 52°?
sin 38°
Use your calculator and round
to the nearest ten thousandth.
sin 48°= ?
sin 48°= .7431
Use your calculator and round
to the nearest hundredth.
cos 79°= ?
cos 79°= .1908
Use your calculator to find the
measure of the angle to the
nearest tenth degree.
tan A= 4.64
tan A = 4.64
77.8°
Use your calculator to find the
measure of the angle to the
nearest tenth degree.
sin B= .5476
sin B= .5476
33.2°
Find the missing value.
If not exact, round to the nearest
hundredth.
𝑥53°
40
𝑥 (hypotenuse)53°
40 (opposite)
50.09 x
x
4053sin
8.4
𝑥
40°
22
Find the missing value.
If not exact, round to the nearest
hundredth.
𝑋(opposite)
40°
22(adjacent)
18.46 x
22
x40tan
8.4
76°
20
𝑥
Find the missing value.
If not exact, round to the nearest
hundredth.
(adjacent)
(hypotenuse)
76°
20
𝑥
82.67 x
x
2076cos
8.4
15
32°
𝑥
Find the missing value.
If not exact, round to the nearest
hundredth.
15(opposite)
32°𝑥
(adjacent)
24.01 x
x
1532tan
8.4
30
Find the missing value.
If not exact, round to the nearest
hundredth.
30 (hypotenuse)
11.24 x
30
x22sin
8.4
Find the missing value.
If not exact, round to the nearest
hundredth.
𝑥° 37
12
18.92 x
37
12xsin
37
12
Remember, you are findingan angle, therefor you useThe key on your calculator
1sin
𝑥°
8.4
Find the missing value.
If not exact, round to the nearest
hundredth.
x
8
17
64.8 x
8
17xtan
Remember, you are findingan angle, therefor you usethe key on your calculator1tan
x
8
17(opposite)
(adjacent)
8.4
Find the missing value.
If not exact, round to the nearest
hundredth.
18
14
x
64.8 x
18
14xcos
Remember, you are findingan angle, therefor you usethe key on your calculator1cos
(hypotenuse)
(adjacent)
18
14
x
Johnny and Jeff are building a skateboard ramp that is
100 centimeters long and rises 75 centimeters. What is
the angle of the ramp (𝑚∠𝐴)?
Johnny and Jeff are building a skateboard ramp that is
100 centimeters long and rises 75 centimeters. What is
the angle of the ramp (𝑚∠𝐴)?(hypotenuse)
(opposite)sin 𝐴 =
75
100
𝐴 = sin−175
100𝐴 = 48.59°
Find the height of the building to the nearest foot.
63°
85 ft
x
Find the height of the building to the nearest foot.
63°
85
xtan 63 =
85
𝑎tan 63𝑎
tan 63=
85
tan 63𝑎 = 43 𝑓𝑡
William is an archaeologist completing field work in Egypt. William
examines an ancient pyramid and determines that each side of the square base
is 220 feet long. The angle of incline of each side of the pyramid is 50°.How tall is the pyramid if the highest point is over the center of the base?
Round your answer to the nearest whole foot.
William is an archaeologist completing field work in Egypt. William
examines an ancient pyramid and determines that each side of the square base
is 220 feet long. The angle of incline of each side of the pyramid is 50°.How tall is the pyramid if the highest point is over the center of the base?
Round your answer to the nearest whole foot.
(opposite)
(adjacent)110
x
tan 50 =𝑥
110𝑥 = 110(tan50)𝑥 = 131 feet
If the quarterback, Q, throws the football 45 yards from one 30-yard line to a
player, P, located on the other 30-yard line, at what angle (∠𝑃𝑄𝑅), to the nearest
degree, did the quarterback have to throw the football?
If the quarterback, Q, throws the football 135 feet from one 30-yard line to a
player, P, located on the other 30-yard line, at what angle (∠𝑃𝑄𝑅), to the nearest
degree, did the quarterback have to throw the football?
cos x =40
45
𝑥 = cos−140
45
𝑥 = 27°
(hypotenuse)
(adjacent)
45
𝑥°40
An observer at the top of a 60 m lighthouse sights two ships approaching, one
behind the other. The angles of elevation of the ships are 30° and 20°. Find the
distance between the ships to the nearest tenth.
An observer at the top of a 60 m lighthouse sights two ships approaching, one behind the other. The angles of
elevation of the ships are 30° and 20°. Find the distance between the ships to the nearest tenth.
30°
60 m
𝑥
20°
60 m
𝑦
tan 30 =60
𝑥tan 30𝑥
tan 30=
60
tan 30𝑥 = 103.9 𝑚
(adjacent)
(adjacent)
(opposite)
(opposite)
tan 20 =60
𝑦tan 20𝑦
tan 20=
60
tan 20𝑦 = 164.8 𝑚
103.9 m
164.8 m
Final answer: 164.8-103.9=60.9 m
What variable represents the length of an adjacent leg
for a 50° angle?
50°
ca
t
What variable represents the length of an adjacent leg
for a 50° angle?
50°
ca
t
t
(adjacent)
(opposite)
(hypotenuse)
25°
do
g
Find the measure of d, if o = 20. Round to the nearest whole.
25°
do
g
Find the measure of d, if o = 20. Round to the nearest whole.
20
(opposite)
(hypotenuse)
sin 25 =20
𝑑𝑠𝑖𝑛25 𝑑
sin 25=
20
sin 25
𝑑 = 47
Find the measure of a, if t = 20. Round to the nearest whole.
50°
c
a
t
Find the measure of a, if t = 20. Round to the nearest whole.
50°
ca
t20
(adjacent)
(opposite)
tan 50 =𝑎
2020 tan 50 = 𝑎
29 = 𝑎
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