Question

The bottom of a ladder that is leaning against a wall makes a 60° angleof elevation with the other end of the ladder. If the ladder is 9 meterlong, at what height does the ladder touch the wall?Round your answer to the nearest tenth of a meter.Required: enter an answer!mSA

Answer 1

Given:

The length of the ladder, l=9 m.

The angle of elevation of the ladder, θ=60°.

Let h be the height at which the ladder touches the wall with respect to the ground.

Now, using trigonometeric property in the above triangle,

`\begin{gathered} \sin \theta=\frac{opposite\text{ side}}{\text{hypotenuse}} \\ \sin \theta=(h)/(l) \end{gathered}`

Substitute the values and solve the equation for h.

`\begin{gathered} \sin 60^(\circ)=(h)/(9) \\ h=9*\sin 60^(\circ) \\ h=7.8\text{ m} \end{gathered}`

Therefore, the ladder touches the wall at a height of 7.8 m.