Aladder 20 feet long leans against a wall and forms an angle of 30° with the ground. how far from the wall is the ladder?

The ladder is 17.32 feet from the wall

Step-by-step explanation:

* Lets explain how to solve the problem

- There is a ladder of length 20 feet

- It leans against a wall and forms an angle of 30° with the ground

- We need to know how far the ladder from the wall

- That means the horizontal distance between the ladder

  and the wall

- Assume that the ladder, the wall and the ground formed a right

 angle triangle LWH, where LH represents the ladder and it is the

 hypotenuse of the triangle , LW represents the wall and  WH

 represents the ground, both of them are the legs of the triangle

 Where W is the right angle

∵ The measure of the angle between the ladder and the ground

  is 30°

∴ m∠LHW = 30°

- In ΔLWH

∵ LH = 20 ⇒ the length of the ladder

∵ m∠LHW = 30°

∵ HW is the adjacent side of ∠LHW

- By using cosien function

∵ cos Ф = adjacent/hypotenuse

∵ Ф = 30°

∵ LH = 20 ⇒ hypotenuse

∴ cos(30) = HW/20

- Multiply both sides by 20

∴ 20 × cos(3) = HW

∴ HW = 10√3 = 17.32

∵ HW represents the horizontal distance between the ladder and

  the wall

∴ The ladder is 17.32 feet from the wall

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step-by-step explanation: