Answer:
The correct option is a) 6.4 m
Step-by-step 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,
[tex]m\angle BAC = 52^{\circ}[/tex]
[tex]m\angle CBA = 40^{\circ}[/tex]
Since, the sum of all interior angles of a triangle is 180°,
[tex]\implies m\angle CAB+m\angle ABC+m\angle ACB=180^{\circ}[/tex]
[tex]52^{\circ}+40^{\circ}+m\angle ACB=180^{\circ}[/tex]
[tex]92^{\circ}+m\angle ACB=180^{\circ}[/tex]
[tex]m\angle ACB=180^{\circ}-92^{\circ}=88^{\circ}[/tex]
Using law of sine,
[tex]\frac{\sin C}{AB}=\frac{\sin B}{AC}[/tex]
[tex]\frac{\sin 88^{\circ}}{10}=\frac{\sin 40^{\circ}}{AC}[/tex]
[tex]\implies AC = \frac{10\sin 40^{\circ}}{\sin 88^{\circ}}=6.43179\approx 6.4[/tex]
Hence, player 1 is 6.4 meters far from the coach.
