Trigonometric Equations Question 19
Question: Two pillars of equal height stand on either side of a roadway which is 60 metres wide. At a point in the roadway between the pillars, the elevation of the top of pillars are 60° and 30°. The height of the pillars is
[UPSEAT 2004]
Options:
A) $ 15\sqrt{3}m $
B) $ \frac{15}{\sqrt{3}}m $
C) $ 15m $
D) $ 20m $
Show Answer
Answer:
Correct Answer: A
Solution:
-
$ \tan 60{}^\circ =\frac{h}{x}\Rightarrow \frac{\sqrt{3}}{1}=\frac{h}{x}\Rightarrow h=\sqrt{3}x $ .....(i) $ \tan 30{}^\circ =\frac{h}{60-x}\Rightarrow \frac{1}{\sqrt{3}}=\frac{h}{60-x}\Rightarrow 60-x=\sqrt{3}h $ .....(ii) From equation (i) and (ii), $ 60-x=\sqrt{3}(\sqrt{3}x) $ $ \frac{60}{4}=x\Rightarrow x=15 $ Then $ h=\sqrt{3}x\Rightarrow h=15\sqrt{3} $ metre.
BETA
