Answer:
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
