A40-foot ladder is leaning against a building and forms a 29.32° angle with the ground. how far away from the building is the base of the ladder? round your answer to the nearest hundredth. 45.88 feet 34.88 feet 22.47 feet 19.59 feet

the base of the ladder is 34.88 feet from the building ⇒ 2nd answer

step-by-step explanation:

* lets explain how to solve the problem

- a 40-foot ladder is leaning against a building

∴ the length of the ladder is 40 feet

- it forms a 29.32° angle with the ground

∴ the angle between the base of the ladder and the ground

    is 29.32°

- consider the building , the ground and the ladder form a right

  triangle the building and the the ground are its legs and the

  ladder is its hypotenuse

∴ the hypotenuse = 40 feet

- to find the distance from the building to the base of the ladder

  use the cosine function because the distance between the

  building and the base of the ladder is adjacent to the given angle

  and we have the length of the hypotenuse

∵ cos ф = adjacent(d)/hypotenuse

∵ ф = 29.32°

∵ the length of the hypotenuse is 40

∴ cos(19.32) = d/40 ⇒ multiply both sides by 40

∴ d = 40 × cos(19.32) = 34.88 feet

* the base of the ladder is 34.88 feet from the building

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step-by-step explanation:

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