A man standing on the roof of a building 56.0 feet high looks down to the building next door. He finds the angle of depression to the roof of that building from the roof of his building to be 34.6°, while the angle of depression from the roof of his building to the bottom of the building next door is 63.7°. How tall is the building next door? (Round your answer to the nearest tenth.)
+128474 Call the height of the neighboring building, H
And call the distance between the buildings = D
So we have that
tan(34°) = [ 56 - H ] / D
D = [56 - H ]/ tan (34°)
And we also have that
tan (63.7) = 56/ D
tan (63.7) = 56 /[ (56 -H) / tan(34) ]
tan (63.7) = 56 tan (34) / [ 56 - H ]
[ 56 - H ] tan (63.7) = 56 tan (34)
56 tan (63.7) - H tan (63.7) = 56 tan (34)
H tan (63.7) = 56 ( tan (63.7) - tan (34) ]
H = 56 [ tan (63.7) - tan (34) ] / tan (63.7) ≈ 37.3 ft
