Algebra 2 - Section 13.1 Right Triangle Trigonometry

Learning Target: I can use trigonometric relationships to evaluate trigonometric

functions of acute angles. [G.SRT.6,8]

Review: Pythagorean Theorem

- Used to find a side length of a right triangle.

a2 + b2 = c2

Find the missing side. Give your answer in simplest radical form.

θ

Consider a right triangle:θ (theta) is an acute angle of a right triangle.

sin θ =

cot θ =sec θ =

tan θ =

csc θ =

cos θ =sine cosine tangent

cosecant secant cotangent

Trigonometric ratio - a ratio that compares the lengths of two sides of a right triangle.

The reciprocal trig ratios:

**across from right angle

**NEXT to

1. Find the cos θ

θ6

2√13

4

2. Find the csc θ.

3. Evaluate the 6 trigonometry functions of the angle Ɵ.

θ1612

4. Given the ratio for cos Ɵ, find the remaining ratios.

** make a ∆

Use a calculator to evaluate the trig. function. Round to 4 decimal places.

5. cos 15˚ = 6. sin 15˚ =

8. cot 62˚ =7. csc 18˚ =

To find a missing side using trig.

1. Pick angle.

2. Label sides for THAT angle.

3. Pick trig ratio.

9. y

x

530˚

Find the missing side lengths. Round to the nearest tenth.

y

10.

11. B = 28˚, a = 6

A

B

C

a

b

c

Solve ∆ABC. (means find all angles and sides)

A = ______

b = ______

c = ______

12. A = 45˚, c = √7

B = ______

a = ______

b = ______

Assignment:Right ∆ - Evaluating trig ratio worksheet

Exit problem:Evaluate the 6 trig functions of angle ⩉. 6

8⩉

≈ 2.3 ≈ 2.3;

≈ 16.2; ≈ 8.1