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

A balloon is directly above one end of a bridge. The angle of depression of the other end of the bridge form the balloon is 48°. If the height of the balloon above the bridge is 122 m, then what is the length of the bridge? Correct Answer 122 tan 42° m

Concept:

  • Angle of depression: The angle of depression is formed when the observer is higher than the object he/she is looking at. When an observer looks at an object that is situated at a distance lower than the observer, an angle is formed below the horizontal line drawn with the level of the eye of the observer and line joining object with the observer’s eye.

 

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  • tan (90 – θ) = cot θ
  • cot (90 – θ) = tan θ


Calculation:

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

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So, Alternate angles ∠ CBA =48°

In triangle ABC,

tan 48° = AC/AB

⇒ AB = AC/ tan 48°

⇒ AB = AC cot 48°

⇒ x = 122 cot (90 – 42)°

⇒ x = 122 tan 42°

∴ Option 2 is correct.

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