Harry is building a house with a sloping roof. if the roof is 44 feet long and 10 feet high, what is the angle that the roof makes with the horizontal? a. 12.8° b. 13.1° c. 14.6° d. 15.3° e. 17.5°

Alright, lets get started.

Please refer the attached diagram.

The roof will make a right angle triangle.

Thy hypotenuse of the triangle will be the length of roof that is given 44 feet.

The opposite side will be height of roof that is 10 feet.

Lets suppose roof makes x degree angle from horizontal.

So, we know,

sin x = opposite / hypotenuse

sin x = 10 / 44

sin x = 0.2272727272

Taking inverse on both sides

sin -1 (sin x) = sin -1 (0.2272727272)

x = sin -1 (0.2272727272)

x = 13.13 degrees

So the angle that roof makes with horizontal is 13.1 degrees (option b) : Answer

Hope it will help :)