From a point A, the angle of elevation to the top of a building is 50°. From point B which is 11 m closer

to the building the angle of elevation to the top is 63°. How far is point B from the top of the building?
How tall is the building?

1 answer

Add point C at bottom of bldg.
AB = 11 m.
Point D is top of bldg.
BD is hyp. of triangle BCD.

h = (BC+11)Tan50 = BC*Tan63.
(BC+11)Tan50 = BC*Tan63.
Divide both sides by tan50:
BC+11 = 1.65BC
BC = 16.9 m. = Hor. leg of rt. triangle.

h = BC*Tan63 = 16.9*Tan63 = 33.2 m. = Ver. leg of rt. triangle.

BD = sqrt(16.9^2+33.2^2) = Distance from point B to top of bldg.

b
h = BC*Tan63.