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NDA 2018
Exam
NDA
Year
2018
Subject
Mathematics
Chapter
Heights and Distances

NDA 2018 · Mathematics · Heights and Distances

A balloon is directly above one end of a bridge. The angle of...

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∘48^{{}^{\circ}}. If the height of the balloon above the bridge is 122 m , then what is the length of the bridge?

Options

  1. A122sin⁡48∘m122 \sin 48^{{}^{\circ}} \mathrm{m}
  2. B122tan⁡42∘m122 \tan 42^{{}^{\circ}} \mathrm{m}
  3. C122cos⁡48∘m122 \cos 48^{{}^{\circ}} \mathrm{m}
  4. D122tan⁡48∘m122 \tan 48^{{}^{\circ}} \mathrm{m}

Correct answer

A. 122sin⁡48∘m122 \sin 48^{{}^{\circ}} \mathrm{m}

Step-by-step solution

Let the bridge is BC and height above the bridge AB=122m\mathrm{AB}=122 \mathrm{ m}.
From △ABC,\triangle \mathrm{ABC},cot⁡48∘=BCAB=BC122BC=122⋅cot⁡(48∘)=122⋅cot⁡(90∘−42∘)=122⋅tan⁡42∘\begin{aligned} & \cot 48^{{}^{\circ}}=\frac{\mathrm{BC}}{\mathrm{AB}}=\frac{\mathrm{BC}}{122} \\ & \mathrm{BC}=122 \cdot \cot \left(48^{{}^{\circ}}\right) \\ &= 122 \cdot \cot \left(90^{{}^{\circ}}-42^{{}^{\circ}}\right) \\ &= 122 \cdot \tan 42^{{}^{\circ}} \end{aligned}$$
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