A ladder 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