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EXAMPLE 5

jcolwell
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EXAMPLE 5

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  1. While standing at Yavapai Point near the Grand Canyon, you measure an angle of 90º between Powell Point and Widforss Point, as shown. You then walk to Powell Point and measure an angle of 76º between Yavapai Point and Widforss Point. The distance between Yavapai Point and Powell Point is about 2 miles. How wide is the Grand Canyon between Yavapai Point and Widforss Point? EXAMPLE 5 Use indirect measurement Grand Canyon

  2. x tan76º = 2 x 8.0 ≈ ANSWER The width is about 8.0 miles. EXAMPLE 5 Use indirect measurement SOLUTION Write trigonometric equation. 2(tan76º) = x Multiply each side by 2. Use a calculator.

  3. A parasailer is attached to a boat with a rope 300 feetlong. The angle of elevation from the boat to the parasailer is 48º. Estimate the parasailer’s height above the boat. EXAMPLE 6 Use an angle of elevation Parasailing

  4. ANSWER The height of the parasailer above the boat is about 223 feet. h sin48º = 300 x 223 ≈ EXAMPLE 6 Use an angle of elevation SOLUTION STEP 1 Draw: a diagram that represents the situation. STEP 2 Write: and solve an equation to find the height h. Write trigonometric equation. 300(sin48º) = h Multiply each side by 300. Use a calculator.

  5. 9. In Example 5, find the distance between Powell Point and Widforss Point. The distance is about 8.27 miles. ANSWER for Examples 5 and 6 GUIDED PRACTICE Grand Canyon

  6. What If? In Example 6, estimate the height of the parasailer above the boat if the angle of elevation is 38°. 10. ANSWER The height of the parasailer above the boat is about 185feet. for Examples 5 and 6 GUIDED PRACTICE

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