Question

3. A ladder that is 20 feet long is leaning against the side of a building. If the angle formed between the ladder and the ground is 75 degrees, how far is the bottom of the ladder from the base of the building?

Answer 1

Distance of bottom of the ladder from the base of the building is 5.18 feet.

Explanation:

Given:

Length of ladder = 20 feet

Angle formed between ladder and ground = 75 degrees.

To Find:

Distance of bottom of the ladder from the base of the building.

Solution:

Consider the below figure forming a triangle ABC.

AB is building

AC is ladder , so AC = 20 feet

BC is distance between base of building and bottom of ladder.

And angle between ground and ladder that is ∠C = 75degrees

Need to calculate BC ,

As triangle ABC forms right angled triangle , right angle at B ,

So
`cos C =( BC)/(AC)`

=> BC = AC cos C

=> BC= 20 cos (75)

=> BC = 5.18 feet

Hence distance of bottom of the ladder from the base of the building is 5.18 feet.