Question

A technician has to repair a light on a pole of height 10 m. She needs to reach a point 2 m below the top of the pole to undertake the repair work. The length of the ramp that she should use which, when inclined at an angle of ${30}^{\circ }$ to the horizontal, would enable her to reach the required position, is______ m.
(You may take $\sqrt{3}$ = 1.73)

• A. 8 m
• B. 16 m
• C. 12 m
• D. 10 m

Answer 1

The correct option is B 16 m

Let BD be the height of the pole. And A is the point where she has to do the repair work.

So, distance of the point she should reach = AB = 10 - 2 = 8 m
In the given right-angled triangle,
$Sin{30}^{\circ }=\frac{AB}{AC}$

$\Rightarrow \frac{1}{2}=\frac{8}{AC}$
Hence, length of the Ramp AC = 2 $\times$ 8 = 16m