Question

A ladder leans against a building, making a 50 degree angle of elevation with the ground. The top of the ladder reaches a point on the building that is 14 feet above the ground. To the nearest tenth of a foot, what is the distance, x between the base of the building and the base of the ladder? If the answer does not have a tenths place then include a zero so that it does. Do not include the units in the answer.

Answer 1

x = 11.8

Explanation:

base of the building and the ground are at 90° to one another.

angle of elevation is 50°. so the angle between building and top of ladder must be 180 - 90 - 50 = 40°.

this is the angle opposite the length x.

50° is opposite height 14.

x/sin 40 = 14/sin 50

x = (14 X sin40)/ sin 50

x = 11.8