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
- A \(d \tan \alpha\)
- B \(d \cot \beta\)
- C \(\frac{d}{\cot \alpha+\cot \beta}\)
- D \(\frac{d}{\cot \alpha-\cot \beta}\)
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 \(\triangle A B D\),…
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