1. Agenda/Objectives Check/go over homework Show the tan -1, cos -1, sin -1 buttons Notes on 8.7 Worksheet problems Prepare for CORE ASSESSMENT

2. 8.7 Applications of Right Triangle Trigonometry

3. Take out your calculators Rather than using the table to look up values, lets use our calculators tan -1 cos -1 sin -1 This will help you find the angle!

4. 1) sin B = 0.4848 2) sin A = 0.5150 3) cos A = 0.7431 4) cos W = 0.6157 5) cos A = 0.5878 6) tan W = 19.0811 7) cos A = 0.4226 8) tan W = 0.5317

5. Definitions Suppose an operator at the top of a lighthouse sights a sailboat on a line that makes a 2° angle with the a horizontal line. The angle between the horizontal and the line of sight is called an angle of depression. At the same time, a person in the boat must look 2° above the horizontal to see the tip of the lighthouse. This is an angle of elevation. BIG QUESTION: WHAT TYPES OF ANGLES ARE THESE AND WHY ARE THEY THE SAME?

6. Finishing the example…. Using the lighthouse as 25 m above sea level, the distance x between the boat and the base of the lighthouse can be found in two ways: Method 1Method 2

7. Example The angle of elevation is 59° and you are 45 feet from the base. Find the height of the tree.

8. The math tan 59 ° = opposite adjacent tan 59 ° = h 45 45 tan 59° = h 45 (1.6643) ≈ h 75.9 ≈ h Write the ratio Substitute values Multiply each side by 45 Use a calculator or table to find tan 59 ° Simplify  The tree is about 76 feet tall.

9. Example From the top of a lighthouse 20 m high, a sailboat is sighted having an angle of depression of 4°. How far from the lighthouse is the boat?

10. Ex. 7: Estimating Distance Escalators. The escalator at the Wilshire/Vermont Metro Rail Station in Los Angeles rises 76 feet at a 30° angle. To find the distance d a person travels on the escalator stairs, you can write a trigonometric ratio that involves the hypotenuse and the known leg of 76 feet. 30 °

11. Now the math 30 ° sin 30 ° = opposite hypotenuse sin 30 ° = 76 d d sin 30° = 76 sin 30 ° 76 d = 0.5 76 d = d = 152 Write the ratio for sine of 30 ° Substitute values. Multiply each side by d. Divide each side by sin 30 ° Substitute 0.5 for sin 30 ° Simplify  A person travels 152 feet on the escalator stairs.

12. Remainder of class Worksheet with partners Core assessment practice Page 318-319 1-9