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Chapter 8.4 and 8.5

Chapter 8.4 and 8.5. Trigonometry and angles of Elevation and Depression. Inverse Trigonometric Ratios. Recall that we used sine, cosine, and tangent to find missing side lengths in right triangles We use inverse trig ratios to find missing angle measures: sine -1 , cos -1 , tan -1 , .

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Chapter 8.4 and 8.5

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  1. Chapter 8.4 and 8.5 Trigonometry and angles of Elevation and Depression

  2. Inverse Trigonometric Ratios • Recall that we used sine, cosine, and tangent to find missing side lengths in right triangles • We use inverse trig ratios to find missing angle measures: sine-1, cos-1, tan-1,

  3. Example 4 Find Angle Measures Using Inverse Trigonometric Ratios Use a calculator to find the measure of P to the nearest tenth.

  4. Example 4 Use a calculator to find the measure of D to the nearest tenth. A. 44.1° B. 48.3° C. 55.4° D. 57.2°

  5. Try it! Find each angle measure. • Pg. 571 #4A and 4B

  6. Example 5 Solve a Right Triangle Solve the right triangle. Round side measures to the nearest hundredth and angle measures to the nearest degree.

  7. Example 5 Solve the right triangle. Round side measures to the nearest tenth and angle measures to the nearest degree. A.mA = 36°, mB = 54°, AB = 13.6 B.mA = 54°, mB = 36°, AB = 13.6 C.mA = 36°, mB = 54°, AB = 16.3 D.mA = 54°, mB = 36°, AB = 16.3

  8. Example 1 Angle of Elevation CIRCUS ACTS At the circus, a person in the audience at ground level watches the high-wire routine. A 5-foot-6-inch tall acrobat is standing on a platform that is 25 feet off the ground. How far is the audience member from the base of the platform, if the angle of elevation from the audience member’s line of sight to the top of the acrobat is 27°? Make a drawing.

  9. Since are parallel, mBAC = mACD by the Alternate Interior Angles Theorem. Example 2 Angle of Depression DISTANCE Maria is at the top of a cliff and sees a seal in the water. If the cliff is 40 feet above the water and the angle of depression is 52°, what is the horizontal distance from the seal to the cliff, to the nearest foot? Make a sketch of the situation.

  10. Example 1 DIVING At a diving competition, a 6-foot-tall diver stands atop the 32-foot platform. The front edge of the platform projects 5 feet beyond the ends of the pool. The pool itself is 50 feet in length. A camera is set up at the opposite end of the pool even with the pool’s edge. If the camera is angled so that its line of sight extends to the top of the diver’s head, what is the camera’s angle of elevation to the nearest degree? A. 37° B. 35° C. 40° D. 50°

  11. Example 2 Luisa is in a hot air balloon 30 feet above the ground. She sees the landing spot at an angle of depression of 34. What is the horizontal distance between the hot air balloon and the landing spot to the nearest foot? A. 19 ft B. 20 ft C. 44 ft D. 58 ft

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