The angle of elevation and depression of the top and bott...
The angle of elevation and depression of the top and bottom of another building, measured from the top of a 24 m tall building, is 30° and 60°, respectively. Determine the second building's height.
A.
24 m
B.
32√3 m
C.
24√3
D.
32 m
Correct answer is D
The height of the second building H = h + 24
tan θ = oppadj
tan 30o=hx
⟹√33=hx
⟹x=√3=3h
⟹x=3h√3 ....(i)
tan 60o=24x
⟹√3=24x
⟹x√3=24
⟹x=24√3 ....(ii)
Equate equation (i) and (ii)
⟹3h√3=24√3
⟹ 3h = 24
⟹h=243 = 8m
∴The height of the second building = 8 + 24 = 32m