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,
[tex]\begin{gathered} \sin \theta=\frac{opposite\text{ side}}{\text{hypotenuse}} \\ \sin \theta=\frac{h}{l} \end{gathered}[/tex]Substitute the values and solve the equation for h.
[tex]\begin{gathered} \sin 60^{\circ}=\frac{h}{9} \\ h=9\times\sin 60^{\circ} \\ h=7.8\text{ m} \end{gathered}[/tex]Therefore, the ladder touches the wall at a height of 7.8 m.
