Trigonometric Equations Question 138
Question: From a 60 meter high tower angles of depression of the top and bottom of a house are a and b respectively. If the height of the house is $ \frac{60,\sin ,(\beta -\alpha )}{x}, $ then x =
Options:
A) $ \sin \alpha \sin \beta $
B) $ \cos \alpha \cos \beta $
C) $ \sin \alpha \cos \beta $
D) $ \cos \alpha \sin \beta $
Show Answer
Answer:
Correct Answer: D
Solution:
- $ H=d\tan \beta $ and $ H-h=d\tan \alpha $
$ \Rightarrow $ $ \frac{60}{60-h}=\frac{\tan \beta }{\tan \alpha } $
$ \Rightarrow $ $ -h=\frac{60\tan \alpha -60\tan \beta }{\tan \beta } $
$ \Rightarrow $ $ h=\frac{60\sin (\beta -\alpha )}{\cos \alpha \cos \beta \frac{\sin \beta }{\cos \beta }} $
$ \Rightarrow $ $ x=\cos \alpha \sin \beta $ .
BETA
