what is the height of the building?

Question

A surveyor determines that the angle of elevation to the top of a building from a point on the ground is 31.9 degrees. He then moves back 43 feet and determines that the angle of elevation is 26.8 degrees. What is the height of the building?Round your answer to four decimal places.

Answer 1

tan 31.9 = h/x

tan 26.8 = h/(x+43)

solve both equations for h:

h = x*tan 31.9 = (x+43)(tan 26.8)

(tan 31.9)x = (tan 26.8)x + 43 (tan 26.8)

(tan 31.9)x - (tan 26.8)x = 43 (tan 26.8)

x [ tan 31.9 - tan 26.8] = 43 (tan 26.8)

x = 43* tan 26.8 / [ tan 31.9 - tan 26.8]

185.15965641706474148503157413698

Finally,

h = tan 31.9 * 185.15965641706474148503157413698

= 115.25173562388322249001045001908