Trigonometric Equations Question 122
Question: A person observes the angle of elevation of a building as 30°. The person proceeds towards the building with a speed of $ 25(\sqrt{3}-1)m/hour. $ After $ 2,hours $ , he observes the angle of elevation as 45°. The height of the building (in meter) is
[UPSEAT 2003]
Options:
A) 100
B) 50
C) $ 50(\sqrt{3}+1) $
D) $ 50(\sqrt{3}-1) $
Show Answer
Answer:
Correct Answer: B
Solution:
- In $ \Delta PQR $ , $ \tan 30^{o}=\frac{PQ}{QR} $
Þ $ \frac{1}{\sqrt{3}}=\frac{h}{50(\sqrt{3}-1)+h} $
Þ $ \sqrt{3}h=50(\sqrt{3}-1)+\sqrt{3}h $ Þ $ (\sqrt{3}-1)h $ $ =50(\sqrt{3}-1) $
Þ $ h=50,\text{m} $
BETA
