"The length of the shadow of a tree is 125 feet when the angle of elevation of the sun is 33 degrees. Approximate the height of the tree." Can't figure this out can anyone help?

1 Answer
Google
May 24, 2018

Its about 81 ft high. The trick to this question is realizing that you can assume the tree makes a right angle with the ground - after that it is just a little bit of trigonometry.

Explanation:

Since we are assuming that the tree makes a right angle with the ground, we can set up a right triangle with these values.

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We know that the tangent function can be used in problems involving the opposite and adjacent sides of the triangle - which we are. The tree forms the opposite side and the ground the adjacent one.

#tan(33)=x/125#

Then, we can multiply both sides of the equation by 125 to isolate x, the height of the tree.

#125tan(33)=x#

#x= 81.1759491497...#

This tells us that, rounded to the nearest foot, the tree is 81 feet high.

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