A 20-foot ladder is leaning against the side of a building. The ladder makes a 60 angle with the building. How far away from the bottom of the building is the foot (bottom) of the ladder?

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Mathematics

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27 July, 06:58

A 20-foot ladder is leaning against the side of a building. The ladder makes a 60 angle with the building. How far away from the bottom of the building is the foot (bottom) of the ladder?

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Nehemiah West · Answer 1

Answer: the distance is 10 feet.

Step-by-step explanation:

The ladder forms a right angle triangle with the building and the ground. The length of the ladder represents the hypotenuse of the right angle triangle. The height from the top of the ladder to the base of the building represents the opposite side of the right angle triangle.

The distance from the foot of the ladder to the bottom of the building, h represents the adjacent side of the right angle triangle.

To determine the distance h, we would apply the cosine trigonometric ratio.

Cos θ = adjacent side/hypotenuse. Therefore,

Cos 60 = h/20

h = 20Cos60 = 20 * 0.5

h = 10 feet