SOLUTION: A man wants to determine the height of a lighthouse. He measured the angle at A and found that tan 3/4. What is the height of the light house if A is 40m from the base?

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Question 1208170: A man wants to determine the height of a lighthouse. He measured the angle at A and found that tan 3/4. What is the height of the light house if A is 40m from the base?
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!

Did you mean to write tan(A) = 3/4?
If so then draw a right triangle with horizontal leg 40, and vertical leg x.

Angle A is the angle of elevation, so it is the angle touching the ground.
Opposite this angle is x.
Adjacent to this angle is 40.

tan(angle) = opposite/adjacent
tan(A) = x/40
x/40 = 3/4
Multiply top and bottom of 3/4 by 10 to arrive at 30/40, which proves x = 30.
The lighthouse is 30 meters tall.

Answer by ikleyn(52915)   (Show Source):
You can put this solution on YOUR website!
.

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