Choose the correct answer of the following question:
A ladder 15 m long makes an angle of 60° with the wall. Find the height of the point, where the ladder touches the wall.
(a) $15 \sqrt{3} \mathrm{~m}$
(b) $\frac{15 \sqrt{3}}{2} \mathrm{~m}$
(c) $\frac{15}{2} \mathrm{~m}$
(d) $15 \mathrm{~m}$
Let AB be the wall and AC be the ladder.
We have,
$\mathrm{AC}=15 \mathrm{~m}$ and $\angle \mathrm{BAC}=60^{\circ}$
In $\triangle \mathrm{ABC}$
$\cos 60^{\circ}=\frac{\mathrm{AB}}{\mathrm{AC}}$
$\Rightarrow \frac{1}{2}=\frac{\mathrm{AB}}{15}$
$\therefore \mathrm{AB}=\frac{15}{2} \mathrm{~m}$
Hence, the correct answer is option (c).
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