Question

Two soccer players on the field are 10 m apart, and their coach is on the sideline. The angle measured from player 1 between player 2 and the coach is 52°. The angle measured from player 2 between player 1 and the coach is 40°. How far is player 1 from the coach?a) 6.4 m b) 7.9 m c) 8.2 m d) 12.3 m

Answer 1

The correct option is a) 6.4 m

Explanation:

Let A represents the position of first player B represents the position of second player and C represents the position of the Coach,

According to the question,

AB = 10 meters,

`m\angle BAC = 52^(\circ)`

`m\angle CBA = 40^(\circ)`

Since, the sum of all interior angles of a triangle is 180°,

`\implies m\angle CAB+m\angle ABC+m\angle ACB=180^(\circ)`

`52^(\circ)+40^(\circ)+m\angle ACB=180^(\circ)`

`92^(\circ)+m\angle ACB=180^(\circ)`

`m\angle ACB=180^(\circ)-92^(\circ)=88^(\circ)`

Using law of sine,

`(\sin C)/(AB)=(\sin B)/(AC)`

`(\sin 88^(\circ))/(10)=(\sin 40^(\circ))/(AC)`

`\implies AC = (10\sin 40^(\circ))/(\sin 88^(\circ))=6.43179\approx 6.4`

Hence, player 1 is 6.4 meters far from the coach.