Question

From the top of a tower 75 m high, the angles of depression of the top and bottom of a pole standing on the same plane as the tower are observed to be ${30}^o$ and ${45}^o$ respectively. Find the height of the pole.

• A. 30.4 m
• B. 35.9 m
• C. 28.6 m
• D. 31.7 m

Answer 1

The correct option is D 31.7 m

Let AB is the tower of height 75 m and CD is the pole, such that $\angle BDE={30}^o$ and $\angle BCA={45}^o$.

In $△BAC,\tan {45}^o=\frac{AB}{AC}$

$1=\frac{AB}{AC}$

$AB=AC$

$AC=75m$

Now, $DE=AC=75m$

In $△BED,\tan {30}^o=\frac{BE}{DE}$

$\frac{1}{\sqrt{3}}=\frac{BE}{75}$

$BE=\frac{75}{\sqrt{3}}$

$BE=25\sqrt{3}=43.3m$

Hence, the height of the pole $=CD=AE=AB-BE=75-43.3=31.7m$