Question

main point on a bridge across a river the angle of depression of the bank on opposite side of river are 30 degree and 45 degree respectively if the bridge is at a height of 2.5 m from the bank find the width of the river.​

Answer 1

The maximum height as AB and draw the angle of depression at two different points and apply tanθ

to the two right angled triangles and we will get two equations and then we have to compute the maximum height from which he falls.

Solution :

Let width of river =AB

And bridge is at height of 3m from banks So, DP=3m

Angel of depression of banks on the opposite sides of the river are 30∘

and 45∘

∠ QPA = 30°

∠ RPB = 45°

Now in triangle PAD

TAN 30° = PA / AD

1/√ 3 = 3/AB

AB = 3√3 ... (i)

Now in triangle PBD

Tan 45° = PD/DE

1 = 3/DE

DB = 3 .... (ii)

width of river = AB= AD +DB

= 3 (√3+1 )

Hence width of river = 3 ( √ 3 + 1 )