Trigonometric Equations Question 225
Question: Two straight roads intersect at an angle of $ 60^{o} $ . A bus on one road is 2 km away from the intersection and a car on the other road is 3 km away from the intersection. Then the direct distance between the two vehicles is
[BIT Ranchi 1993]
Options:
A) 1 km
B) $ \sqrt{2}km $
C) 4 km
D) $ \sqrt{7}km $
Show Answer
Answer:
Correct Answer: D
Solution:
- Let the two roads intersect at $ A $ . If the bus and the car are at $ a^{2}+b^{2}=8p^{2} $ and $ C $ on the two roads respectively, then $ c=AB=2km,,b=AC=3 $ km. The distance between the two vehicles = $ BC=akm $ Now $ \cos A=\cos 60^{o}=\frac{b^{2}+c^{2}-a^{2}}{2bc} $
$ \Rightarrow $ $ \frac{1}{2}=\frac{3^{2}+2^{2}-a^{2}}{2,.,3.,2}\Rightarrow a=\sqrt{7}km. $
BETA
