Ramesh and Sohan start walking away from each other from a point P at an angle of 120°. Ramesh walks at a speed of 3 kmph while Sohan walks at a speed of 4 kmph. What is the distance between them after 90 minutes?
Explanation:
Let Ramesh and Sohan reach points R and S respectively after 90 minutes. ∴ PR = distance travelled by Ramesh in 90 minutes = 1.5 × 3 = 4.5 km Similarly, PS = 1.5 × 4 = 6 km Now, PRS forms a triangle, where two sides (PR and PS) as well as the included angle (RPS = 120°) are known. Hence, the third side can be found using the cosine rule. ∴ Cos 120 = [(4.5)2 + (6)2 − (RS)2] / (2 × 4.5 × 6) ∴ −0.5 = [20.25 + 36 − (RS)2] / 54 ∴ 56.25 − (RS)2 = −27 ∴ (RS)2 = 83.25 i.e. RS = 9.12 Hence, they are 9.12 km apart. Hence, option (c).
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