A 26-ft ladder leans against a building so that the angle between the ground and the ladder is 78°. How high does the ladder reach up the side of the building? (Round your answer to four decimal places.)

Question

Mathematics

Kelsie

23 May, 22:58

A 26-ft ladder leans against a building so that the angle between the ground and the ladder is 78°. How high does the ladder reach up the side of the building? (Round your answer to four decimal places.)

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Answers (1)

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Rene Wolfe · Answer 1

The height of the ladder above the ground is 25.4306 ft

Step-by-step explanation:

The length of the ladder represents the hypotenuse of the right angle triangle.

The ground distance from the base of the building to the foot of the ladder represents the adjacent side of the right angle triangle.

Therefore, to determine how high up is the top of the ladder from the ground, x which represents the opposite side of the right angle triangle, we would apply trigonometric ratio,

Sin θ = opposite side/hypotenuse

Sin 78 = x/26

x = 26Sin78 = 26 * 0.9781

x = 25.4306 ft