Trigonometric Equations Question 212
Question: The top of a hill observed from the top and bottom of a building of height h is at the angle of elevation p and q respectively. The height of the hills is
[UPSEAT 2001; EAMCET 1989]
Options:
A) $ \frac{h\cot q}{\cot q-\cot p} $
B) $ \frac{h\cot p}{\cot p-\cot q} $
C) $ \frac{h\tan p}{\tan p-\tan q} $
D) None of these
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Answer:
Correct Answer: B
Solution:
- Let AD be the building of height h and BP be the hill then $ \tan q=\frac{h+x}{y} $ and $ \tan p=\frac{x}{y} $
Þ $ ,\tan q=\frac{h+x}{x\cot p} $
$ \Rightarrow x\cot p=(h+x)\cot q $
Þ $ x=\frac{h\cot q}{\cot p-\cot q} $
Þ $ h+x=\frac{h\cot p}{\cot p-\cot q} $ .
BETA
