The angel of elevation of the top of a building is found to be 10 degrees from the ground at a distance of 4500 feet from the base of the building. Find the height of the building.

Question

The angel of elevation of the top of a building is found to be 10 degrees from the ground at a distance of 4500 feet from the base of the building.  Find the height of the building.

anonymous · Answer

Trig... Make a triangle out of it. Use your definition of sine, cosine, and tangent (SOH CAH TOA) to solve for the unknown side length of the triangle that you need...

anonymous · Answer

$$h=4500 tan({10\over90}{\pi \over 4}) $$h=393.70 rounded to 1/100

anonymous · Answer

Made a small mistake in the solution above.  The fraction above should be pi/2 not pi/4 in order to convert 90 degrees to radians.     I am using Mathematica for this problem and it is primarily geared for angles expressed in radians.
pi/2 is equivalent to 90 degrees and we want 1/9th of pi/2 which is pi/18.

10 would be OK if one's calculator or paper tangent table was oriented to degrees.   I am using Mathematica for this problem and it is mostly setup to handle angles expressed in radians. 
$$h=4500*\tan({10\over90}{\pi \over 2}) = 4500*\tan({\pi \over 18})$$
h = 793.47 for the building height in feet.