Trigonometric Equations Question 153
Question: From a point a metre above a lake the angle of elevation of a cloud is a and the angle of depression of its reflection is b. The height of the cloud is
[Roorkee 1983; EAMCET 1983, 85]
Options:
A) $ \frac{a\sin ,(\alpha +\beta )}{\sin ,(\alpha -\beta )} $ metre
B) $ \frac{a\sin ,(\alpha +\beta )}{\sin ,(\beta -\alpha )} $ metre
C) $ \frac{a\sin ,(\beta -\alpha )}{\sin ,(\alpha +\beta )} $ metre
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
- $ (H+a)\cot \beta =(H-a)\cot \alpha $ $ H=\frac{a\sin (\alpha +\beta )}{\sin (\beta -\alpha )} $ Using $ \cot \alpha +\cot \beta =\frac{\sin (\alpha +\beta )}{\sin \alpha \sin \beta } $ and $ \cot \alpha -\cot \beta =\frac{\sin (\beta -\alpha )}{\sin \alpha \sin \beta } $ .
BETA
