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Word Problem Exercises: Angles of Depression #2

Question Group #1
Directions and/or Common Information: If a plane that is cruising at an altitude of 30,000 feet wants to land at DBIA, it must begin its descent so that the angle of depression to the airport is 7°.

How many miles from the airport must the plane begin descending?

How far will the plane actually travel to touch down?

General Questions

Find the angle of depression.

A ship is sighted from a lighthouse at Port Richey at an angle of depression of 15°.  How far from Port Richey is the ship if the lighthouse is 52 meters high?

From the top of a 35 meter cliff, Lori spots a hiker at an angle of depression of 62°.  How far away is Lori from the hiker? 

Lauren was standing on the pier at the beach approach trying to find her sister.  She spotted her at the water’s edge at an angle of depression of 28°.  If the pier is 5 yards above the sand, how far down the beach is Lauren’s sister?

Josee wanted to measure the depth of the sink hole that opened on Amelia Avenue this morning.  She measured the angle of depression to the lowest point to be 35°.  She also measured the distance across the sinkhole to be 38 feet.  Assuming the deepest point to be in the exact middle of the sinkhole, how deep is the sinkhole?

Clayton is on the fourth floor of a burning building.  The stairs are blocked and the elevator is not working.  He finds a window whose base, he estimates, is 34 feet above the ground.  He can see the fire truck through the window at an angle of depression of 42°.  If the base of the ladder is 5 feet above the ground, how long must the ladder be extended to reach Clayton?

Ryan was skiing at Snow Bowl, Arizona last winter.  He was at the top of Sunset Peak.  He measured the angle of depression to the bottom of the run to be 14°.  He read that the actual length of the run is 2675 feet.  What is the change in altitude to the bottom of the run?

K Dodd

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