NIMCET 2012 — Mathematics PYQ

Let $AB$ and $CD$ be two towers of heights $h_1$ and $h_2$ respectively. Let $M$ be the mid-point of the line $BD$ joining their feet.

Since $M$ is the mid-point, the distance from each tower to the point $M$ is equal. Let $BM=MD=x$.

Step 2: Apply Trigonometry to the first tower

In the right-angled triangle formed by the first tower ($h_1$) and the mid-point $M$:

Since $\tan (60^{\circ })=\sqrt{3}$, we have:

Step 3: Apply Trigonometry to the second tower

In the right-angled triangle formed by the second tower ($h_2$) and the mid-point $M$:

Since $\tan (30^{\circ })=\frac{1}{\sqrt{3}}$, we have:

Step 4: Find the ratio $h_1:h_2$

Divide Equation 1 by Equation 2:

Conclusion:

The ratio $h_1:h_2$ is $3:1$.

Correct Option: (d)