From A, due east of the building, the angle of elevation of the top is 45 degree. From B, southwest of the building, the angle of elevation is 30 degree. If AB=250m, find the height of the building.

Answer 1

let C be the third vertex of the horizontal triangle, directly below the building

for the vertical triangles, height = AC(tan(45)) = BC(tan(30)) = AC, since tan(45) = 1

now use law of cosines on the horizontal triangle to obtain

250^2 = AC^2 + (AC/tan(30))^2 – 2(AC)(AC/tan(30))cos(135)

and solve the quadratic equation to obtain AC = height = 98.4413

Answer 2

jolly rancher, you are correct sir. Thank you sir