Question

Two buildings are 35 feet apart. The angle of elevation from the top of the smaller building to the top of the taller building is 42˚. The smaller building is 32 feet high. Find the height of the taller building.

Answer 1

Height of the taller building is 63.5ft

Explanation:

Kindly find attached rough sketch of the problem for your reference.

Let the small building be A and the taller building be B

From the sketch the two buildings form a right angle triangle

We can solve for x which is the height of the taller building relative to the small building using

SOH CAH TOA

Applying TOA we have

Tan θ= opposite/adjacent

Tan 42°= x/35

x= Tan 42*35

x= 0.9*35

x= 31.5ft

Hence the height of the taller building is = x+height of small building = 31.5+32= 63.5ft