SOLUTION: At a distance of 300 feet from the base of a building, the angle of elevation to the top of the building is 42 degrees. From the same distance, the angle of elevation to the top of

Question 728461: At a distance of 300 feet from the base of a building, the angle of elevation to the top of the building is 42 degrees. From the same distance, the angle of elevation to the top of a flagpole mounted on the top of the building is 48 degrees. Find the height of the flagpole. Also how can I draw a triangle that describes the situation? Note: We are using right triangles and sin cos tan and their inverses. I just thought I would let you know considering there is probably multiple ways of doing this.
Thank you for the help!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
At a distance of 300 feet from the base of a building, the angle of elevation to the top of the building is 42 degrees. From the same distance, the angle of elevation to the top of a flagpole mounted on the top of the building is 48 degrees. Find the height of the flagpole. Also how can I draw a triangle that describes the situation? Note: We are using right triangles and sin cos tan and their inverses.
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Draw the picture.
You have a right triangle with base = 300 and base angle = 42 degrees.
Let height be "b", which is the height of the building.
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You have a 2nd right triangle with base = 300 and base angle = 48 degrees
Let the height be "f" which is the height of building + flagpole.
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1st: figure the height of the building:
tan(42) = b/300
b = 300*tan(42)
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2nd: figure the height of "f":
f = 300*tan(48)
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Then height of the flagpole = f-b = 300(tan(48)-tan(42)) = 63.06 ft.
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Cheers,
Stan H.
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