PreCalculus - Santowski 1 Lesson 26 - Review of Right Triangle Trigonometry PreCalculus – Santowski

PreCalculus - Santowski 1

Lesson 26 - Review of Right Triangle Trigonometry

PreCalculus – Santowski


(A) Review of Right Triangle Trig

Trigonometry is the study and solution of Triangles. Solving a triangle means finding the value of each of its sides and angles. The following terminology and tactics will be important in the solving of triangles.

Pythagorean Theorem (a2+b2=c2). Only for right angle triangles

Sine (sin), Cosecant (csc or 1/sin) Cosine (cos), Secant (sec or 1/cos) Tangent (tan), Cotangent (cot or 1/tan) Right/Oblique triangle


(A) Review of Right Triangle Trig

In a right triangle, the primary trigonometric ratios (which relate pairs of sides in a ratio to a given reference angle) are as follows:

sine A = opposite side/hypotenuse side & the cosecant A = cscA = h/o cosine A = adjacent side/hypotenuse side & the secant A = secA = h/a tangent A = adjacent side/opposite side & the cotangent A = cotA = a/o

recall SOHCAHTOA as a way of remembering the trig. ratio and its corresponding sides

(B) Review of Trig Ratios

Evaluate and interpret:

(a) sin(32°) (b) cos(69°) (c) tan(10°) (d) csc(78°) (e) sec(13°) (f) cot(86°)

Evaluate and interpret:

(a) sin(x) = 0.4598 (b) cos(x) = 0.7854 (c) tan(x) = 1.432 (d) csc(x) = 1.132 (e) sec(x) = 1.125 (f) cot(x) = 0.2768

4PreCalculus - Santowski

(C) Review of Trig Ratios and Triangles


(C) Review of Trig Ratios and Triangles



(B) Examples – Right Triangle Trigonometry Using the right triangle trig ratios, we can solve for

unknown sides and angles:

ex 1. Find a in ABC if b = 2.8, C = 90°, and A = 35°

ex 2. Find A in ABC if c = 4.5 and a = 3.5 and B = 90°

ex 3. Solve ABC if b = 4, a = 1.5 and B = 90°

(B) Review of Trig Ratios

If sin(x) = 2/3, determine the values of cos(x) & tan(x)

If cos(x) = 5/13, determine the value of sin(x) + tan(x)

If tan(x) = 5/8, determine the sum of sin(x) + 2cos(x)

If tan(x) = 5/9, determine the value of sin2(x) + cos2(x)

A right triangle with angle α = 30◦ has an adjacent side X units long. Determine the lengths of the hypotenuse and side opposite α.


Examples – Right Triangle Trigonometry




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(E) Examples – Right Triangle Trigonometry A support cable runs from the top of the telephone pole

to a point on the ground 43 feet from its base. If the cable makes an angle of 32.98º with the ground, find (rounding to the nearest tenth of a foot): a. the height of the pole b. the length of the cable

43 FEET

POLE

mABC = 32.98

B C

A

PreCalculus - Santowski

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(E) Examples – Right Triangle Trigonometry Mr Santowski stands on

the top of his apartment building (as part of his super-hero duties, you know) and views a villain at a 29º angle of depression. If the building I stand upon is 200 m tall, how far is the villain from the foot of the building?

BUILDING

ANGLE OF DEPRESSION = 29

mADB = 29

A

C D

E

B


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(E) Examples – Right Triangle Trigonometry You are hiking along a

river and see a tall tree on the opposite bank. You measure the angle of elevation of the top of the tree and find it to be 46.0º. You then walk 50 feet directly away from the tree and measure the angle of elevation. If the second measurement is 29º, how tall is the tree? Round your answer to the nearest foot.

TREE

mADB = 29mABC = 46

A

C DB



1404/18/23 Math SL1 - Santowski











Examples – Right Triangle Trigonometry (8) While driving towards a mountain, Mr S

notices that the angle of elevation to the peak is 3.5º. He continues to drive to the mountain and 13 miles later, his second sighting of the mountain top is 9º. Determine the height of the mountain.






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PreCalculus - Santowski 1 Lesson 26 - Review of Right Triangle Trigonometry PreCalculus – Santowski