Question

a 20 foot ladder against a building that makes an angle of 72 with the ground.find to the nearest foot the distance between the foot of the ladder and the building.

Answer 1

Hello from MrBillDoesMath

Answer:   6.2 feet

           

Discussion:

The ladder and the wall form a right triangle. The length of the ladder, 20 in this case, is the hypotenuse of the triangle. Let  "x" be the distance between the foot of the ladder and the building. Then from trigonometry,

cos (@) = length of adjacent side/ hypotenuse  

or in our case

cos(72) =  x / 20 =>            (multiply both sides by 20)

20 * cos(72) = x.

Using a calculator this becomes

20 *  ( .3090) =   6.18 feet  (approx)   or 6.2 feet , rounded to the nearest foot.

Thank you,

Mr. B