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TS EAMCET · Maths · Heights and Distances

The angle of elevation of an object from a point \(P\) on the level ground is \(\alpha\). Moving \(d\) metres on the ground towards the object, the angle of elevation is found to be \(\beta\). Then the height (in metres) of the object is

  1. A \(d \tan \alpha\)
  2. B \(d \cot \beta\)
  3. C \(\frac{d}{\cot \alpha+\cot \beta}\)
  4. D \(\frac{d}{\cot \alpha-\cot \beta}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{d}{\cot \alpha-\cot \beta}\)

Step-by-step Solution

Detailed explanation

Let the height of the object is \(h\). In \(\triangle A B C\), \(\begin{aligned} & \tan \alpha=\frac{h}{x+d} \\ & \Rightarrow \quad x+d=h \cot \alpha \\ & \end{aligned}\) And in \(\triangle A B D\),…