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

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

Using trigonometry, the hiker can find the height: ? = ___________; 7920 = ___________; ________ is 40 0 ; which trig ratio should he use? ___________ x = _________ Similar problem: could a person standing on the mountain looking at the hiker find how high they are? The looks of the triangle may have change but the _______________ and _________________ have not! ANGLE OF ____________! oppositeadjacentangle tangent 40 x ft. Depression ft. ? NumbersRelationships

Solving Elevation/Depression 1.DRAW A __________ 2.Identify a ________ _________ 3.Find angle of __________________ 4.Identify _______ (opposite, adjacent, or hypotenuse 5.Write equation : _______________ 6.________ PICTURE righttriangle elevation or depression sides SOH-CAH-TOA Solve

Example 5-2e 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? Answer: The roller coaster car was about 285 feet above the ground.

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 Example 5-1a Make a drawing Label Identify Equation Solve

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