High School

A private plane is flying 200 feet above the ground, approaching a runway. The angle of depression to the nearest end of the runway is 20 degrees, and the angle of depression to the farthest end of the runway is 12 degrees. How long is the runway? Round to the nearest foot.

Answer :

see the attached picture to better understand the problem

we know that
in the right triangle ABC
tan 20°=AB/AC-----> AC=AB/tan 20----> AC=200/tan 20---> AC=549.50 ft

in the right triangle ABD
tan 12°=AB/AD----> AD=AB/tan 12----> AD=200/tan 12----> AD=940.93 ft

the runway is=DC
DC=AD-AC----> DC=940.93-549.50----> DC=391.43 ft---> 391 ft

the answer is
the runaway is 391 ft long

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