5 Minute Check on Chapter 2 Transparency 3

5 -Minute Check on Chapter 2 Transparency 3 -1 1. Evaluate 42 - |x - 7| if x = -3 2. Find 4. 1 (-0. 5) Simplify each expression 3. 8(-2 c + 5) + 9 c 4. (36 d – 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. Standardized Test Practice: A 8/4 < 4/8 B Which of the following is a true statement -4/8 < -8/4 C -4/8 > -8/4 Click the mouse button or press the Space Bar to display the answers. D -4/8 > 4/8

Lesson 11 -7 Trigonometric Ratios

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

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

Vocabulary • • • Trigonometric ratios – sine – cosine – tangent – angle of elevation – angle of depression –

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?

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.

Example 1 cont Answers: Answer:

Example 1 cont Answers: Answer:

Example 2 Find cos 65° to the nearest ten thousandth. Keystrokes COS 65 ENTER. 4226182617 Answer: Rounded to the nearest ten thousandth,

Example 3 Find the measure of to the nearest degree. Since the lengths of the adjacent leg and the hypotenuse are known, use the cosine ratio. and Now use [COS– 1] on a calculator to find the measure of the angle whose cosine ratio is 12 / 20 Keystrokes 2 nd [COS– 1] 12 20 ENTER 53. 13010235 Answer: To the nearest degree, the measure of is 53°.

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

Example 4 cont 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. Definition of sine Evaluate sin 62°. Find the cross products. is about 17. 0 centimeters long.

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.

Example 5 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. Explore In the diagram two right triangles are formed. You know the height of the airplane and the horizontal distance it has traveled. Plan Let A represent the first angle of depression. Let B represent the second angle of depression.

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

Summary & Homework • Summary: – xxxxx • Homework: – none