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Lesson 9-3: Angles of Elevation & Depression

Learn how to use the angles of elevation and depression in trigonometry to find heights and distances without measuring. Solve real-life problems with step-by-step examples.

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Lesson 9-3: Angles of Elevation & Depression

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  1. Lesson 9-3: Angles of Elevation & Depression Horizontal Angle of depression Height Height Angle of elevation Horizontal

  2. Using Angle of Elevation & Depression Trigonometry can be used to find lengths without actually having to measure. ? ANGLE OF ______________! 400 Elevation 7920 ft. A map tells this hiker the _____________ distance to a mountain is 1.5 miles (or 7920 ft.). horizontal An instrument tells him the angle to look up to see the peak of the mountain is ____________. 40 degrees Can the hiker tell the __________ of the mountain? height

  3. Using trigonometry, the hiker can find the height: ? = ___________; 7920 = ___________; ________ is 400; which trig ratio should he use? opposite adjacent angle ___________ tangent x 40 x = _________ 6646 ft. 7920 Similar problem: could a person standing on the mountain looking at the hiker find how high they are? 7920 ft. 400 ? ANGLE OF ____________! Depression The looks of the triangle may have change but the _______________ and _________________ have not! Numbers Relationships

  4. Solving Elevation/Depression • DRAW A __________ • Identify a ________ _________ • Find angle of __________________ • Identify _______ (opposite, adjacent, or hypotenuse • Write equation : _______________ • ________ PICTURE right triangle elevation or depression sides SOH-CAH-TOA Solve

  5. Example 1 A roller coaster car is at one of its highest points. It drops at a angle for 320 feet. How high was the roller coaster car to the nearest foot before it began its fall? Example 5-2e Answer: The roller coaster car was about 285 feet above the ground.

  6. Example 5-1a Example 2 At the circus, a person in the audience 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 Make a drawing Label Identify Equation Solve

  7. Example 5-1c Answer: The audience member is about 60 feet from the base of the platform.

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