Do Now Find the ratios for sin A, cos A, and tan A. Make sure you simplify as much as possible 2. Find the ratios for sin C, cos C, and tan C. Make sure you simplify as much as possible.

Using Trig to Find Missing Angles and Missing Sides

Today’s Essential Understanding Ratios can be used to find side lengths and angle measures of a right triangle when certain combinations of side lengths and angle measurements are known.

Skills Check

Finding a missing angle Finding a missing angle. (Figuring out which ratio to use and an inverse trig button.)

Steps: 1. Place the theta symbol in the angle you are trying to find 2. Identify the sides as opposite, adjacent, or hypotenuse 3. Based on what side lengths you are given, figure out which ratio to use. 4. Solve for your angle (or theta).

Represents an unknown angle Greek Letter q Prounounced “theta” Represents an unknown angle

What is the measure of angle X to the nearest degree? Let’s Try One! What is the measure of angle X to the nearest degree?

Ex: 1. Figure out which ratio to use. Find x Ex: 1 Figure out which ratio to use. Find x. Round to the nearest tenth. O 20 m 40 m A x Shrink yourself down and stand where the angle is. Identify the given sides as H, O, or A. What trig ratio is this?

Ex: 2. Figure out which ratio to use. Find x Ex: 2 Figure out which ratio to use. Find x. Round to the nearest tenth. O H 15 m 50 m x Shrink yourself down and stand where the angle is. Identify the given sides as H, O, or A. What trig ratio is this?

Ex. 3: Find . Round to the nearest degree. 17.2 9 A

Ex. 4: Find . Round to the nearest degree. 7 23 H

Ex. 5: Find . Round to the nearest degree. 200 O 400 H

Finding a missing side. (Figuring out which ratio to use and getting to use a trig button.)

Steps: 1. Based on the angle you are given, identify the side length you are given and place an X on the side you are trying to find. 2. Figure out which ratio to use. 3. Solve for your missing side.

Ex. 1: Find the value of x. Round to the nearest tenth.

Ex. 2: Find the value of x. Round to the nearest tenth.

Your Turn! Work with your group members to complete the rest of the practice problems. When you are done, start on your homework. Anything you don’t finish will be homework and is due next class. Make sure you are working quietly and efficiently!

Ex: 1. Figure out which ratio to use. Find x Ex: 1 Figure out which ratio to use. Find x. Round to the nearest tenth. 20 m x A O

Ex: 2 Find the missing side. Round to the nearest tenth. 80 ft x O A

Ex: 3 Find the missing side. Round to the nearest tenth.

Ex: 4 Find the missing side. Round to the nearest tenth. 20 ft x A

When we are trying to find a side we use sin, cos, or tan. When we are trying to find an angle we use (INVERSE) sin-1, cos-1, or tan-1.