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Question
Two vehicles leave the same place P at the same time moving along two different roads. One vehicle moves at an average speed of 60 km/hr and the other vehicle moves at an average speed of 80 km/hr. After half an hour the vehicle reaches destinations A and B. If AB subtends 60° at the initial point P, then find AB
Solution
P – Initial point.
PA – The direction of the first vehicle travels with speed km/hr.
PB – The direction of the second vehicle travels with a speed of 80 km/hr.
Given in half an hour first vehicle reaches destination A.
∴ PA = `60/2` = 30 km.
Also in half an hour the second vehicle reaches the destination B.
∴ PA = `80/2` = km.
In ∆PAB,
PA = 30, PB = 40, ∠APB = 60°
Using cosine formula
AB2 = PA2 + PB2 – 2PA PB cos ∠APB
AB = 302 + 402 – 2 × 30 × 40 cos 60°
= `900 + 1600 - 2400 xx 1/2`
= 2500 – 1200
AB2 = 1300
AB = `sqrt(1300)`
= `sqrt(13 xx 100)`
AB = `10sqrt(13)` km.
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