Trigonometry question?

Question

A surveyor measures the angle of elevation of the top of a perpendicular building as 19◦. He moves 120 m nearer the building and finds the angle of elevation is now 47◦. Determine the height of the building in meters

Answer 1

  A surveyor measures 

 the angle of elevation of the top of a perpendicular building as 19°. 

 He moves 120 m nearer the building and finds the angle of elevation is now 47°.   Determine the height of the building in meters

 Let x be the original distance to the building and let h be the height of the building.   Initially we have an angle of 19°: tan(19°) = h/x. Moving 120 m closer, so that the   distance to the building is x - 120, we have an angle of 47°: tan(47°) = h/(x - 120).

 Tan(19°) = 0.3443 and tan(47°) = 1.0723 so we have h/x= 0.3443 which gives h =   0.3443x. That makes the second equation 1.0723 = 0.3443x/(x - 120).

 x ≈ 176.753 m, h = 60.8560579 m