Question 57

The angles of elevation of the top of a tower 72 metre high from the top and bottom of a building are $$30^\circ$$ and $$60^\circ$$ respectively. What is the height (in metres) of building?

Solution

Let say, height of building is x meter.

So, Distance between Building and Tower = $$\frac{72}{\tan60^{\circ\ }}=\frac{72}{\sqrt{3}}=24\sqrt{3}\ .$$

Now, we can say that :

$$\frac{\left(72-x\right)}{24\sqrt{3}}=\tan30^{\circ\ }\ .$$

or, $$\frac{\left(72-x\right)}{24\sqrt{3}}=\frac{1}{\sqrt{3}}\ .$$

or, $$x=72-24=48\ .$$

D is correct choice.

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