Right Triangle Trigonometry

Section 14.3

Objectives…

1. To identify the “parts” of a right triangle

2. To learn the “definitions” (formulas) for each of the trigonometric functions

3. To find either unknown side lengths and/or angle measurements in a right triangle by using the trig functions or their inverses

“The Basics”

Based upon that…

we can use the following formulas to find the values of the six trig functions:

A way to remember…

The word “sohcahtoa” is a commonly used way of remembering the formulas:

- “soh”: sin equals opposite over hypotenuse

- “cah”: cos equals adjacent over hypotenuse

- “toa”: tan equals opposite over adjacent

Remember one thing…

the trig values that you find are based upon one of the three angles being the “reference” angle (if asked to find sin A, angle A is the “reference angle”)

The “opposite” and “adjacent” sides are based upon what this reference angle is (can change)

therefore, sin A may not equal sin B!

Let’s do a basic problem… In triangle ABC, angle C is a right

angle and sin A = 5/13. Find the following trig ratios in fractional form:

- cos A: - tan B: - csc A: - sec B: - cot B:

Let’s do some more…

In triangle DEF, angle F is a right angle, EF = 13, and angle D = 42°. Find the measure of DE to the nearest tenth.

In triangle GHI, angle I is a right angle, GI = 11, and HI = 19. Find the measure of angle H to the nearest tenth of a degree.

Now you try some…

In triangle JKL, angle L is a right angle, KL = 4, and JK = 10. Find the measure of angle J to the nearest tenth of a degree.

In triangle MNO, angle O is the right angle, angle M = 23°, and MN = 23. Find the measure of NO to the nearest tenth.

Now about the lowercase letters… In a diagram, the side opposite the

angle is labeled with the lowercase (side opposite angle A is labeled as a, side opposite angle B is labeled as b, etc…)

Now let’s put this all together… In triangle PQR, angle R is the right

angle, r = 41, and q = 40. Find the remaining sides and angles of the triangle to the nearest tenth.

In triangle STU, angle U is the right angle, angle S = 56°, and t = 7. Find the remaining sides and angles of the triangle to the nearest tenth.

Word Problems!

phrases that you will need to “identify” in order to accurately draw the diagram: “angle of elevation” and “angle of depression”

A man 6 feet tall is standing 50 feet from a tree. When he looks at the top of the tree, the angle of elevation in relation to the ground is 42°. Find the height of the tree to the nearest foot.

Another one…

Mr. Salen is heading to Washington D.C. with the intention of attaching a slide cable from the top of the Washington Monument to the ground. The angle of elevation the cable would make with the ground is 27°. If the Washington Monument is 555 feet tall, how much cable is he going to need?

And another…

Alex is traveling in a hot-air balloon. There is a horse running in a pasture 3500 feet away horizontally from her. If her angle of depression is 35°, how high is the balloon and Alex from the ground rounded to the nearest foot?

One more…

On the planet Salen, with accordance to planetary law, the end of a 20-foot wheelchair ramp cannot be any higher than 18 inches off the ground. What is the maximum angle of elevation that the ramp can make with the ground in order to comply with the law?

Homework!

Assignment #1: pgs. 782-783, #’s 2-7, 18-24, 34-40

Assignment #2: pgs. 783-784, #’s 1, 8, 41-44, 48, 52, 53