AP EAMCET · Maths · Heights and Distances
A vertical pole subtends an angle \(\tan ^{-1}\left(\frac{1}{2}\right)\) at a point \(P\) on the ground. If the angles substended by the upper half and the lower half of the pole at \(P\) are respectively \(\alpha\) and \(\beta\), then \((\tan \alpha, \tan \beta)\) is equal to
- A \(\left(\frac{1}{4}, \frac{1}{5}\right)\)
- B \(\left(\frac{1}{5}, \frac{2}{9}\right)\)
- C \(\left(\frac{2}{9}, \frac{1}{4}\right)\)
- D \(\left(\frac{1}{4}, \frac{2}{9}\right)\)
Answer & Solution
Correct Answer
(C) \(\left(\frac{2}{9}, \frac{1}{4}\right)\)
Step-by-step Solution
Detailed explanation
Let \(A C\) be a pole and point \(P\) be the position on of the ground. Given, \(\theta=\tan ^{-1} \frac{1}{2}\) \(\Rightarrow \quad \tan \theta=\frac{1}{2}\) Also, \(\quad \theta=\alpha+\beta\)…
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