Answer:

Given :-

• A bridge is situated at right angle to the bank of the river. If one moves away a certain distance from the bridge along this side of the river, the other end of the Bridge is seen at an angle of 45° and if someone moves a further distance of 400 metres in the same direction, the other end is seen at an angle of 30°.

To Find :-

• The length of the bridge.

Solution :-

Suppose, the length of the bridge AB = x m.

In ∆ ABC,

➛ tan 45° =

➛ 1 =

➡ BC = x ..... (1)

Again,

⇒ tan 30° =

⇒

➦ BC = AB√3 - 400 .... (2)

From (1) and (2) we get,

Let, x = AB√3 - 400

➟ x - x√3 = - 400

➟ x√3 - x = 400

➟ x(√3 - 1) = 400

➟ x =

➟ x =

➟ x =

➟ x =

➟ x = 200(1.732 + 1)

➟ x = 200 × 2.732

➠ x = 546.4

The length of the bridge is 546.4 m.

Answer:

The length of the bridge 546.4 m