Prasitha has two buildings A and B. A is 10 feet shorter than the twice the height of B. The distance between the buildings is 120 feet and the height of B is 60 feet. Find the distance between their tops.

The distance between their tops is 130 feet

Step-by-step explanation:

The given parameters are;

The height of A, = 2 × The height of B - 10

The distance between the two buildings, d = 120 feet

The height of B, = 60 feet

Therefore, we have;

The height of A,  = 2 × The height of B - 10 = 2 × 60 - 10 = 110 feet

The height of A, = 110 feet

By Pythagoras theorem, the distance between their tops = √(( - )² + d²)

Substituting the values gives;

The distance between their tops = √((110 - 60)² + 120²) = 130

The distance between their tops = 130 feet.

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