Question

answer this question from points A and B on level ground the angles of elevation of the top of a building are 25° and 37° respectively. if |AB|=57m,calculate, to the nearest metre, the distances of the top of the building from A and B if they are both on the same side of the building

Answer 1

If you draw the diagram and review your basic trig functions, then if the height is h, it becomes clear that
h cot25° - h cot37° = 57
h = 57/(cot25° - cot37°) = 69.73m

Answer 2

Tan25 = h/x
h =x*Tan25.

Tan37 = h/ (x-57)
h = (x-57)Tan37.

h = x*Tan25 = (x-57)Tan37
x*Tan25 = (x-57)Tan37
x*Tan25 = x*Tan37-57*Tan37
0.467x = 0.754x-43.
X = 150 m. = hor. distance from point A to foot of bldg.
x-57 = 150-57 = 93 m. = hor. distance from point B to foot of bldg.
h = x*Tan25 = 150*Tan25 = 70 m. = ht. of bldg.

sin25 = h/r = 70/r
r = 166 m. = distance from point A to top of bldg.

sin37 = h/r = 70/r
r = 116 m. = distance from point B to top of bldg.