Exploring Trigonometric Ratios In this unit you will

Exploring Trigonometric Ratios In this unit, you will learn how to 1) Use sine, cosine, and tangent ratios to determine side lengths in right triangles 2) Use sine, cosine, and tangent ratios to find angle measures in right triangles

The Trig Ratios n Trig ratios relate sides of a right triangle to one of the acute angles

Using The Sine Ratio In the right triangle ABC below,

Using the Cosine Ratio In the right triangle ABC below,

Practice 1 In the right triangle ABC below, find sin B, cos B, sin C, and cos C. ANSWERS:

Using the Tangent Ratio In the right triangle ABC below,

Practice 2 n In the right triangle below, find tan B and tan C Answers: tan B = 12/5 tan C = 5/12

Finding Side Lengths Example A Find the value of x. Round to the nearest tenth. HINT! To start, identify how the sides relate to the given angle. Then decide which trig ratio to use Side x is opposite of the given angle. The given side is the hypotenuse. USE THE SINE RATIO!

Finding Side Lengths Example B Find the value of x. Round to the nearest tenth. HINT! To start, identify how the sides relate to the given angle. Then decide which trig ratio to use Side x is the hypotenuse. The given side is adjacent to the given angle. USE THE COSINE RATIO!

Work With A Partner n Find a partner and solve practice problems 11 -A 4. 6 12. 9 6. 2 2

Finding Missing Angles n To find missing angles, you must know the inverses of the trig functions

Finding Missing Angles Example A n Find the measure of angle. Round to the nearest tenth. HINT: The given sides are the hypotenuse and the side adjacent to the missing angle USE COSINE RATIO!

Finding Missing Angles Example B n Find the measure of angle. Round to the nearest tenth. HINT: The given sides are the opposite side and the side adjacent to the missing angle USE TANGENT RATIO!

Work With A Partner n Find a partner and solve practice problems 11 -B 22. 6 o 17. 1 o 48. 2 o 50 o