Expert: Sherman D. - 11/11/2005

Question
Mr. Reigle observes that the angle of elevation of the top of a building is 41degrees35minutes. after moving back a distance of 256 feet, Mr. Riegle finds taht the angle of elevation to the top of the building is now28degrees17minutes. Find the height of the building.

Answer
It sometimes helps to draw it out.

Here are the values used

x = distance from the building
y = height of building

tan(28°17') = y1/(x + 256)
this is (x + 256) since he moved 256 ft back from "x" distance he was from the building already.

tan(28°17') = y1/(x + 256)
y1 = tan(28°17')(x + 256)

tan(41°35') = y2/x
y2 = tan(41°35')x

since the height of the building will remain the same, just set y1 and y2 equal to each other

tan(28°17')(x + 256) = tan(41°35')x
tan(28°17')x + 256tan(28°17') = tan(41°35')x
tan(41°35')x - tan(28°17')x = 256tan(28°17')
(tan(41°35') - tan(28°17'))x = 256tan(28°17')
x = (256tan(28°17'))/(tan(41°35') - tan(28°17'))

work that all out and you get

x = (137°44'44.7")/(0°53'14.36" - 0°32'17.05")
x = (137°44'44.7")/(0°20'57.31")
x = (137.7457559)/(.349252136)
x = 394.4020421

ANS : The building is about 394 feet tall.