Trigonometric Equations Question 121
Question: From the bottom of a pole of height h, the angle of elevation of the top of a tower is $ \alpha $ and the pole subtends angle $ \beta $ at the top of the tower. The height of the tower is
[Roorkee 1988]
Options:
A) $ \frac{h\tan (\alpha -\beta )}{\tan (\alpha -\beta )-\tan \alpha } $
B) $ \frac{h\cot (\alpha -\beta )}{\cot (\alpha -\beta )-\cot \alpha } $
C) $ \frac{\cot (\alpha -\beta )}{\cot (\alpha -\beta )-\cot \alpha } $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
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$ d=H\cot \alpha $ $ d=(H-h)\cot (\alpha -\beta ) $
$ \Rightarrow $ $ H\cot \alpha $ $ =(H-h)\cot (\alpha -\beta ) $ or $ H=\frac{h\cot (\alpha -\beta )}{\cot (\alpha -\beta )-\cot \alpha } $ .
BETA
