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The straight roads intersect at an angle...

The straight roads intersect at an angle of 60°. A bus on one road is 2 km away from the intersection and a car on tire other road is 3 km away from the intersection. Then, the direct distance between the two vehicles, is

A

1 km

B

`sqrt2` km

C

4 km

D

`sqrt7` km

Text Solution

Verified by Experts

Let the two roads intersect at A. If the bus and the car are at B and C on the two roads respectively then c = AB = 2 km, b = AC = 3 km. The distance between the two vehicles = BC = a km.
Now,
`A=60^(@)`
`rArrcosA=cos60^(@)rArr(b^(2)+c^(2)-a^(2))/(2bc)=1/2rArra=sqrt7` km
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