A ladder leans against a house at a 60° angle to the ground. If the ladder extends to a length of 166 inches, what is the height of the house to the nearest hundredth of an inch?

Answer 1

No idea. Does the ladder reach the roof? If so, and it does not extend beyond the edge of the roof (see how poorly posed the problem is?)

sin60° = height/length

height = 0.866 * 166 = 143.76 in.

Answer 2

A ladder leans against a house at a 60° angle to the ground.

House with a ladder measuring 166 inches forming a right triangle. The base angle formed by the ladder is 60 degrees.

If the ladder extends to a length of 166 inches, what is the height of the house, rounded to the nearest hundredth of an inch?