SOLUTION: The angle of depression from the top of a flagpole on top of a lighthouse to a boat on the ocean is 37 degrees, while the angle of depression from the bottom of the flagpole to the

Algebra ->  Pythagorean-theorem -> SOLUTION: The angle of depression from the top of a flagpole on top of a lighthouse to a boat on the ocean is 37 degrees, while the angle of depression from the bottom of the flagpole to the      Log On


   

Question 118990: The angle of depression from the top of a flagpole on top of a lighthouse to a boat on the ocean is 37 degrees, while the angle of depression from the bottom of the flagpole to the boat is 36.8 degrees. If the boat is 1 mile away from shore and the lighthouse is right on the edge of the shore, how tall is the flagpole?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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e angle of depression from the top of a flagpole on top of a lighthouse to a boat on the ocean is 37 degrees, while the angle of depression from the bottom of the flagpole to the boat is 36.8 degrees. If the boat is 1 mile away from shore and the lighthouse is right on the edge of the shore, how tall is the flagpole?
:
First find the height of the top of the flagpole to sea level
A right triangle formed by this side (Let it = a) and the 1 mile distance to the boat>
We want the height of the flagpole in feet. Change 1 mi to feet: 5280 ft
:
Find the interior angle at the top of the triangle: 90 - 37 = 53 degrees
:
Using the tangent of 53 degrees
a = 5280%2F%28tan%2853%29%29
a = 3978.8 ft is the top of the flagpole above sea level
:
Find the height above sea-level of the base of the flagpole, Let this side = b
:
Find the interior angle at the base of the triangle: 90 - 36.8 = 53.2 degrees
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Using the tangent of 53.2 degrees
b = 5280%2F%28tan%2853.2%29%29
b = 3950 ft is the base of the flagpole above sea level
:
Flag pole = a - b
3978.8 - 3950 = 28.8 ft is the height of the flagpole