Question

A ladder 5 m long, leaning against a vertical wall makes

an angle of 65° with the ground. How far up the wall is
the top of the ladder?

Answer 1

The height of the top of the ladder from the ground is 4.53 m

Explanation:

Given:

length of ladder =5 m

Angle formed = 65°

Let h be the Height of the top of the ladder from the ground

Required:

Height of the top of the ladder from the ground

Equation:

SOH-CAH-TOA

Since the hypotenuse side is given and what we are to solve is the opposite side, use SOH

`sinθ\:=\: (opposite)/(hypotenuse)`

`sin(65°)\:=\: (opposite)/(5\: m)`

`opposite\:=\:(5 \:m )\:sin(65°)`

`opposite\:=\:4.53 \:m`

Final Answer:

The height of the top of the ladder from the ground is 4.53 m

Please refer to the photo for the illustration