Simon leans a 20 ft ladder against the side of his house so that the base of the ladder is 5 ft from the house. About how high up the side of the house does the ladder reach? Round to the nearest tenth of a foot?

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

it would open into a square depending on the type of envelope i’m not sure about the second part

it is a secret for it not to be compromised sorry

step-by-step explanation: