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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

Sagot :

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.

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