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A ladder of a fire truck is elevated to an angle of $60^{\circ}$ and extended to a length of $70 feet$ . If the base of the ladder is $7 feet$ above the ground, how many feet above the ground does the ladder reach?

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(8 + 35 \sqrt{3})

(8 - 35 \sqrt{3})

(7 - 35 \sqrt{3})

(7 + 35 \sqrt{3})

answer is D.

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Detailed Solution

It is given that a ladder of a fire truck is elevated to an angle of

60^{\circ}

and extended to a length of

70 feet

. The base of the ladder is

7 feet

above the ground.
Question Image

△ BAC,

\sin 60 ° = \frac{AC}{AB} = \frac{AC}{70}

⇒

\frac{\sqrt{3}}{2} = \frac{AC}{70}

⇒

AC = \frac{70 \sqrt{3}}{2}

⇒

AC = 35 \sqrt{3}

∴

The ladder reaches

(7 + 35 \sqrt{3}) m

above the ground.
Hence, the correct option is 4.

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