Two straight roads intersect at an angle of 6 | vedclass

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Question

(D) Let the intersection point of the two roads be $A$. Let the position of the bus be $B$ and the position of the car be $C$.Given that $AB = 2 \, km

Vedclass · Accepted Answer

$\sqrt{7} \, km$

Vedclass · Answer

(D) Let the intersection point of the two roads be $A$. Let the position of the bus be $B$ and the position of the car be $C$.Given that $AB = 2 \, km$,$AC = 3 \, km$,and the angle $\angle BAC = 60^o$.Using the Law of Cosines in $	riangle ABC$:$BC^2 = AB^2 + AC^2 - 2(AB)(AC) \cos(60^o)$$BC^2 = 2^2 + 3^2 - 2(2)(3) \left(\frac{1}{2}ight)$$BC^2 = 4 + 9 - 6$$BC^2 = 7$$BC = \sqrt{7} \, km$.Thus,the direct distance between the two vehicles is $\sqrt{7} \, km$.

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

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