Question

36. An aeroplane at an altitude of 200 m observers the angles of depression of
opposite point on the two banks of a river to be 450 and 600. Find the width of
the rever.​

Answer 1

Answer:

Heyaa♡♡

In ΔABC:-

$tan45 = \frac{p}{b} \\ = > 1 = \frac{y}{200} \\ = > y = 200$

Now, In ΔABD:-

$tan30 = \frac{p}{b} \\ = > \frac{1}{ \sqrt{3} } = \frac{x}{200} \\ = > x = \frac{200}{ \sqrt{3} }$

Then,

$width = x + y \\ = > 200 + \frac{200}{ \sqrt{3} } \\ = > 200(1 + \frac{1}{ \sqrt{3} } ) \\ = > 200( \frac{ \sqrt{3} + 1}{ \sqrt{3} } ) \\ = > 200( \frac{1.732 + 1}{1.732} ) \\ = > 200 (\frac{2.732}{1.732} ) \\ = > 200(1.577) \\ = > 315.2$

So, the width of the river is approx. 315 m.

Hope it helped you.