A 24-foot ladder forms a 76 angle with the ground. The top of the ladder rests against a building. To the nearest foot, how high up the building does the ladder reach?

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Mathematics

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1 May, 08:41

A 24-foot ladder forms a 76 angle with the ground. The top of the ladder rests against a building. To the nearest foot, how high up the building does the ladder reach?

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Peter Little · Answer 1

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, h 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 bottom of the ladder to the base of the building represents the adjacent side of the right angle triangle.

To determine the the height, h that the ladder reaches, we would apply

the Sine trigonometric ratio.

Sin θ, = opposite side/hypotenuse. Therefore,

Sin 76 = h/24

h = 24Sin76 = 24 * 0.97

h = 23.28 feet