Question 56

The angles of elevation of the top of a tree 220 meters high from two points lie on the same plane are $$30^\circ$$ and $$45^\circ$$. What is the distance (in metres) between the two points?

Solution

We can draw following picture :

So, $$\tan30^{\circ\ }=\frac{222}{a+b}\ .$$

or, $$a+b=220\sqrt{3}\ .$$

And, $$\tan45^{\circ\ }=\frac{220}{a}\ .$$

or, $$a=220\ .$$

So, Distance between these two points = $$220\left(\sqrt{3}-1\right)=161.05\ .$$

D is correct choice.

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