Question

1) 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°. Let us find the length of the bridge.
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Answer 1

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° = $\dfrac{AB}{BC}$

➛ 1 = $\dfrac{x}{BC}$

➡ BC = x ..... (1)

Again,

⇒ tan 30° = $\dfrac{AB}{BD}$

⇒ $\dfrac{AB}{BC+ 400} =\: \dfrac{1}{\sqrt{3}}$

➦ 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 = $\dfrac{400}{\sqrt{3} - 1}$

➟ x = $\dfrac{400(√3 + 1)}{(√3 - 1)(√3 + 1)}$

➟ x = $\dfrac{400(√3 - 1)}{3 - 1}$

➟ x = $\dfrac{400(√3 - 1)}{2}$

➟ x = 200(1.732 + 1)

➟ x = 200 × 2.732

➠ x = 546.4

$\therefore$ The length of the bridge is 546.4 m.

Answer 2

Answer:

The length of the bridge 546.4 m