Q= Two ships leave a port at the same time One goes 24 km/h in the direction N45oE and - Maths - Trigonometric Functions

Question

Q= Two ships leave a port at the same time One goes
24 km/h in the direction N45oE and the other travels 32
km/h in the direction S75oE Find the distance b/w the
ships at the end of 3 hours

Ankush Jain · Accepted Answer

Let A and B be two positions of the ships at the end of 3 hours.

$\Rightarrow OA = 3 \times 24 = 72 k m and OB = 3 \times 32 = 96 km$

In ΔOAB, by cosine formula, we have

${(AB)}^{2} = {OA}^{2} + {OB}^{2} - 20 A \times OB \cos 60 ° {(AB)}^{2} = (72)^{2} + (96)^{2} - 2 \times 72 \times 96 \times \frac{1}{2} \Rightarrow {(AB)}^{2} = 5184 + 9216 - 6912 = 7488 \Rightarrow AB = \sqrt{7488} km = 86.53 km$

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Q= Two ships leave a port at the same time .One goes 24 km/h in the direction N45oE and the other travels 32 km/h in the direction S75oE.Find the distance b/w the ships at the end of 3 hours.

Q= Two ships leave a port at the same time .One goes 24 km/h in the direction N45^oE and the other travels 32 km/h in the direction S75^oE.Find the distance b/w the ships at the end of 3 hours.