Question

From a point on a bridge across river, the angles of depression of the banks on opposite sides of river are 30° and 45°, respectively. If bridge is at a height of 3m, Find width of river.

50PTS.

Answer 1

Hey there!

In the figure above ↑↑
A and B represent points on the banks on opposite sides of River.
So, AB is width.

Height of brigde, DP = 3m

Now,
AB = AD + DB

In right triangle ABD, Angle A = 30°

So,

tan30° = PD/AD

$\frac{1}{ \sqrt{3} } = \frac{3}{AD}$

$AD \: = 3 \sqrt{3} m$

In triangle PBD, Angle B = 45°
So BD = PD = 3m

Now,
AB = DB + AD

$3 + 3 \sqrt{3}$

$3( \sqrt{3 + 1} )m$

Hence, The width of river is:

$3( \sqrt{3 + 1} )m$

HOPE IT HELPED ^_^
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Answer 2

The width of the river is 8.19