Let’s Get It Started . . . 30° 60° A B C

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Presentation transcript:

Let’s Get It Started . . . 30° 60° A B C What is the correct term for side AB, opposite right C? What is the side opposite B? What is the leg side adjacent to B? What is the side opposite A? What is the leg side adjacent to A? hypotenuse AC BC

Introduction to Trigonometry Section 9.1 Introduction to Trigonometry At the end of this lesson you will understand/apply: sine (sin) cosine (cos) tangent (tan)

Three Trigonometric Ratios Only for RIGHT triangles!!!!!

SOHCAHTOA or SohCahToa B 5 3 C A 4

Why? To solve triangles other than 30°-60°-90° or 45°-45°-90°. Look on page 424 in your textbook at the Table of Trigonometric Ratios. You have the luxury of using a calculator! IMPORTANT: Your calculator must be in DEGREE mode.

Communicating 1. What happens to sin A as A increases? The sin A increases. 2. As A increases, what number is sin A approaching? 1 Or, the sin A approaches 1 as the measure of A approaches 90. 3. Can you state/write a generalization similar to above that describes the relationship between the cos A and the measure of A. The cos A approaches 1 as the measure of A approaches 0.

New Vocabulary A Angle of elevation: The angle between an upward line of sight and the horizontal. P of elevation H P H Angle of depression: The angle between a downward line of sight and the horizontal. of depression B IMPORTANT: These angles are between a line of sight and the horizontal. Do NOT use the vertical!

Using Trigonometric Ratios to Find a Missing Side 40 Find missing side to nearest whole number. x 27

Using Trigonometric Ratios to Find a Missing Side (cont.) Find missing side to nearest whole number. x 32 70

Using Trigonometric Ratios to Find a Missing Side (cont.) 60 x Find missing sides to nearest hundredth. y 4

Using Trigonometric Ratios to Find a Missing Angle Find missing angles to nearest hundredth. b 7 a 24

Using Trigonometric Ratios to Find a Missing Angle (cont.) Find missing angles to nearest tenth. b 9 a 12

Using Trigonometric Ratios to Solve a Word Problem A boat is pulling a parasailer. The line to the parasail is 800 feet long. The angle between the line and the water is about 25. (a) How high is the parasailer? (b) How far back is the parasailer from the boat? 800 25