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.

Height of the taller building is 63.5ft

Step-by-step 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

damm bro the struggle

step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4