1. 5-Minute Check on Chapter 2 Transparency 3-1 Click the mouse button or press the Space Bar to display the answers. 1.Evaluate 42 - |x - 7| if x = -3 2.Find 4.1  (-0.5) Simplify each expression 3. 8(-2c + 5) + 9c 4. (36d – 18) / (-9) 5.A bag of lollipops has 10 red, 15 green, and 15 yellow lollipops. If one is chosen at random, what is the probability that it is not green? 6. Which of the following is a true statement Standardized Test Practice: ACBD 8/4 < 4/8-4/8 < -8/4-4/8 > -8/4-4/8 > 4/8

2. Lesson 11-7 Trigonometric Ratios

3. Transparency 7 Click the mouse button or press the Space Bar to display the answers.

4. Transparency 7a

5. Objectives Define the sine, cosine, and tangent ratios Use trigonometric ratios to solve right triangles

6. Vocabulary Trigonometric ratios – sine – cosine – tangent – angle of elevation – angle of depression –

7. Four Step Problem Solving Plan Step 1: Explore the Problem –Identify what information is given (the facts) –Identify what you are asked to find (the question) Step 2: Plan the Solution –Find an equation the represents the problem –Let a variable represent what you are looking for Step 3: Solve the Problem –Plug into your equation and solve for the variable Step 4: Examine the Solution –Does your answer make sense? –Does it fit the facts in the problem?

8. Example 1 Find the sine, cosine, and tangent of each acute angle of Round to the nearest ten-thousandth. Write each ratio and substitute the measures. Use a calculator to find each value.

9. Example 1 cont Answers: Answer:

10. Example 1 cont Answers: Answer:

11. Example 2 Answer: Rounded to the nearest ten thousandth, Find cos 65° to the nearest ten thousandth. Keystrokes COS ENTER 65.4226182617

12. Example 3 and Since the lengths of the adjacent leg and the hypotenuse are known, use the cosine ratio. Now use [COS –1 ] on a calculator to find the measure of the angle whose cosine ratio is 12 / 20 Find the measure of to the nearest degree. Answer: To the nearest degree, the measure ofis 53°. [COS –1 ] ENTER 53.13010235 12 Keystrokes 20 2nd

13. Example 4 Step 1 Find the measure ofThe sum of the measures of the angles in a triangle is 180. The measure of is 28°. You need to find the measures of and Find all of the missing measures in

14. Example 4 cont Definition of sine Evaluate sin 62°. Find the cross products. is about 17.0 centimeters long. Step 2 Find the value of y, which is the measure of the hypotenuse. Since you know the measure of the side opposite use the sine ratio.

15. Example 4 cont Step 3 Find the value of x, which is the measure of the side adjacent Use the tangent ratio. Definition of sine Evaluate tan 62°. Find the cross products. is about 8.0 centimeters long. Answer: So, the missing measures are 28 , 8 cm, and 17 cm.

16. Example 5 ExploreIn the diagram two right triangles are formed. You know the height of the airplane and the horizontal distance it has traveled. PlanLet A represent the first angle of depression. Let B represent the second angle of depression. Indirect Measurement In the diagram, Barone is flying his model airplane 400 feet above him. An angle of depression is formed by a horizontal line of sight and a line of sight below it. Find the angles of depression at points A and B to the nearest degree.

17. Example 5 cont and SolveWrite two equations involving the tangent ratio. Answer: The angle of depression at point A is 45° and the angle of depression at point B is 37°.

18. Summary & Homework Summary: –xxxxx Homework: –none