Trigonometric Equations Question 177
Question: From an aeroplane vertically over a straight horizontally road, the angles of depression of two consecutive mile stones on opposite sides of the aeroplane are observed to be a and b, then the height in miles of aeroplane above the road is
[MNR 1986; UPSEAT 1999]
Options:
A) $ \frac{\tan \alpha ,.,\tan \beta }{\cot \alpha +\cot \beta } $
B) $ \frac{\tan \alpha +\tan \beta }{\tan \alpha ,.,\tan \beta } $
C) $ \frac{\cot \alpha +\cot \beta }{\tan \alpha ,.,\tan \beta } $
D) $ \frac{\tan \alpha ,.,\tan ,\beta }{\tan \alpha +\tan \beta } $
Show Answer
Answer:
Correct Answer: D
Solution:
- $ d_1=h\cot \alpha $ and $ d_2=h\cot \beta $ $ d_1+d_2=1 $ mile = $ h(\cot \alpha +\cot \beta ) $
$ \Rightarrow $ $ h=\frac{1}{(\cot \alpha +\cot \beta )}=\frac{\tan \alpha .\tan \beta }{\tan \alpha +\tan \beta } $ .
BETA
