To measure the height of Lincoln'scaricature on Mt. Rushmore, two sightings 800 feet apart from thebase of the mountain are taken. If the angle of evelation to thebottom of Lincoln's face is 32 degrees and the angle of elevationto the top of his face is 35 degrees, what is the height ofLincoln's face?

Jadon Melendez

Jadon Melendez

Answered question

2022-07-31

To measure the height of Lincoln'scaricature on Mt. Rushmore, two sightings 800 feet apart from thebase of the mountain are taken. If the angle of evelation to thebottom of Lincoln's face is 32 degrees and the angle of elevationto the top of his face is 35 degrees, what is the height ofLincoln's face?

Answer & Explanation

Jazlene Dickson

Jazlene Dickson

Beginner2022-08-01Added 15 answers

It is helpful if you draw a triangle. Since tan = opp/adj, we get:
tan ( 32 ) = x / 800
and
tan ( 35 ) = y / 800
Where x is the distance from the ground to the bottom of his face,and y is the distance from the ground to the top of his face. If we solve these two equations, we get x = 499.90 and y =560.17. We simply need to subtract these to find the heightof his face: 60.27 feet.

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