Two buildings are 60 feet apart across a street. a person on top of the shorter building finds the angle of elevation of the roof of the taller building to be 20 degrees and the angle of depression of its base to be 35 degrees. how tall is the taller building to the nearest foot?

The height of the taller building is

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the value of h1

with the angle of elevation

we know that

step 2

Find the value of h2

with the angle of depression

we know that

step 3

Find the height of the taller building

The height of the taller building is the sum of h1 plus h2

so

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

just sum

10 + 10 = 20