4.3 Applications Involving Right Triangles

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Objective - To use basic trigonometry to solve right triangles.

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Presentation transcript:

4.3 Applications Involving Right Triangles At the end of this lesson you will understand/apply: sin and sin-1 cos and cos-1 tan and tan-1 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?

Three Trigonometric Ratios Only for RIGHT triangles!!!!! SOHCAHTOA or SohCahToa

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? 2. As A increases, what number is sin A approaching? 3. Can you state/write a generalization similar to above that describes the relationship between the cos A and the measure of A.

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 x 57 Find missing side to nearest tenth. 10.8 37 x Find missing side to nearest tenth. 11

Using Trigonometric Ratios to Find a Missing Side (cont.) Find missing side to nearest tenth. x 32 13

Using Trigonometric Ratios to Find a Missing Angle Find missing angle to nearest tenth.  5 4 13 12

Using Trigonometric Ratios to Find a Missing Angle (cont.) Find missing angle to nearest tenth. 7.7 14

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