What is the height of the building?

Question

the angle of elevation to a building is 17°. 50 meters closer the the building, the angle of elevation is 31°. What is the height of the building?

Answer 1

we have an angle of elevation 31 degrees from a distance  x  from the base of the building

we have an angle of elevation 17 degrees from a distance  x+50 from the base of the building

(distance in meters) we have tan31 = h/x = 0.6008  --->>> h=0.6008x (h is the heigh of the building)

we have tan17=h/(x+50) = 0.3057  --->>> h=0.3057(x+50)  h=0.3057x + 15.285

so we have 0.6008x = 0.3057x + 15.285   ---->>>. 0.2951x = 15.285  --->>>  x = 15.285 / 0.2951 = 51.796

so the h = 0.6008x = 0.6008 * 51.796 = 31.119   so heigh of the building = 31.119 m  (approx)

the same result of course we have from h=0.3057(51.796)+15.285 = 31.119 m (approx)