Two ships leave a port from a point at the sa | vedclass

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Question

(A) Let the starting point be $O$. After $2 	ext{ hours}$, the distance travelled by the first ship is $OA = 3 	ext{ km/h} 	imes 2 	ext{ h} = 6

Vedclass · Accepted Answer

$2 \sqrt{13}$

Vedclass · Answer

(A) Let the starting point be $O$. After $2 	ext{ hours}$, the distance travelled by the first ship is $OA = 3 	ext{ km/h} 	imes 2 	ext{ h} = 6 	ext{ km}$.The distance travelled by the second ship is $OB = 4 	ext{ km/h} 	imes 2 	ext{ h} = 8 	ext{ km}$.The angle between the two paths is $\angle AOB = 45^{\circ} + 15^{\circ} = 60^{\circ}$.Using the Law of Cosines in $	riangle AOB$:$AB^2 = OA^2 + OB^2 - 2(OA)(OB) \cos(60^{\circ})$$AB^2 = 6^2 + 8^2 - 2(6)(8) 	imes \frac{1}{2}$$AB^2 = 36 + 64 - 48$$AB^2 = 100 - 48 = 52$$AB = \sqrt{52} = \sqrt{4 	imes 13} = 2 \sqrt{13} 	ext{ km}$.

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