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**Pre-AP Pre-Calculus Chapter 4, Section 8**

Solving Problems with Trigonometry

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Right Angle Problems Angle of elevation: the angle through which the eye moves up from horizontal to look at something above Angle of depression: the angle through which the eye moves down from horizontal to look at something below.

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**Using Angle of Depression**

The angle of depression of a buoy from the top of the Barnegat Bay lighthouse 130 feet above the surface of the water is 6°. Find the distance from the base of the lighthouse to the buoy.

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**Making Indirect Measurements**

From the top of the 100-ft-tall Altgelt Hall a man observes a car moving toward the building. If the angle of depression of the car changes from 22° to 46° during the period of observation. How far does the car travel?

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**Finding Height Above Ground**

A large, helium-filled penguin is moored at the beginning of a parade route awaiting the start of the parade. Two cables attached to the underside of the penguin makes angles of 48° and 40° with the ground and are in the same plane as a perpendicular line from the penguin to the ground. If the cables are attached to the ground 10 feet from each other, how high above the ground is the penguin?

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**Finding a Cathedral Height**

The angle of elevation of the top of the Ulm Cathedral from a point 300 ft away from the base of its steeple on level ground is 60°. Find the height of the cathedral.

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Finding a Distance The angle of depression from the top of the Smoketown Lighthouse 120 ft above the surface of the water to a buoy is 10°. How far is the buoy from the lighthouse?

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Cloud Height To measure the height of a cloud, you place a bright searchlight directly below the cloud and shine the beam straight up. From a point 100 ft away from the searchlight, you measure the angle of elevation of the cloud to be 83°12’. How high up is the cloud?

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Civil Engineering The angle of elevation from an observer to the bottom edge of the Delaware River drawbridge observation deck located 200 ft form the observer is 30°. The angle of elevation from the observer to the top of the observation deck is 40°. What is the height of the observation deck?

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