oak tree height. i got 44.9 but idk if i am right. could u please explain. thanks

Question

you want to know the approximate height of a tall oak tree. you place a mirror on the ground and stand where you can see the top of the tree in the mirror. how tall is the tree? the mirror is 24 feet from the base of the tree. you are 36 inches from the mirror and your eyes are five feet above the ground. round your answer to the nearest tenth.

Answer 1

Hi Chayll, we know the height of the tree will equal 24 times the tangent of the angle found from the information given.

 

The tangent is the opposite side divided by the adjacent side of a right triangle. Here we are given the distance you are standing from the mirror (36 inches or 3 feet), the adjacent side, and the height of your eyes (5 feet above the ground) the opposite side.

 

The angle is the tan^-1 of 5/3, which is 59.04 degrees.

 

The height of the tree is 24 * tan(59.04) or about 40.0 feet.

 

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