Question

A balloon is directly above one end of a bridge.The angle of depression of the other end of the bridge from the balloon is 48°.If the height of the balloon above the bridge is 122 m, then what is the length of the bridge ?

Answer 1

Refer to the attached image.

Let AC be the height of the balloon above the bridge  = 122 meters

Since, the angle of depression of the other end of the bridge from the balloon is 48°.

Let the length of the bridge = AB = 'x' meters

So, $\angle DCB = 58^\circ$

Also, $\angle DCB = \angle CBA$ (Alternate angles)

So, $\angle CBA = 48^\circ$

In triangle ABC,

$\angle ACB + \angle BAC + \angle CBA = 180^\circ$

$\angle ACB + 90^\circ + 48^\circ = 180^\circ$

$\angle ACB = 42^\circ$

Now, in triangle ABC,

Consider $\tan C = \frac{P}{B}$

$\tan 42^\circ = \frac{AB}{AC}$

$\tan 42^\circ = \frac{x}{122}$

$x =122 \tan 42^\circ$

Therefore, the length of the bridge is $x =122 \tan 42^\circ$ meters.

So, option B is the correct answer.