Question

Two soccer players are warming up by kicking soccer balls at a goalie. The two players are located 10 yards apart, and the angle from each player to the goalie is 64° and 75°, respectively. What is the distance from the farthest soccer player to the goalie?


10.747 yards

13.700 yards

14.723 yards

24.447 yards

Answer 1

Using the law of sines, it is found that the distance from the farthest soccer player to the goalie is 14.723 yards.

What is the law of sines?

Suppose we have a triangle in which:

• The length of the side opposite to angle A is a.

• The length of the side opposite to angle B is b.

• The length of the side opposite to angle C is c.

The lenghts and the sine of the angles are related as follows:

$\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}$

In this problem, considering that the sum of the internal angles of a triangle is of 180º, the angle that the goalie makes with the players is given by:

$A_g = 180 - (64 + 75) = 41$

Then, the situation can be represented by the graph given at the end of this problem.

Thus, applying the law of sines, we have that:

$\frac{\sin{41^\circ}}{10} = \frac{\sin{75^\circ}}{d_{p1}} = \frac{\sin{64^\circ}}{d_{p2}}$

Then, the player 1 distance is:

$\frac{\sin{41^\circ}}{10} = \frac{\sin{75^\circ}}{d_{p1}}$

$d_{p1} = \frac{10\sin{75^\circ}}{\sin{41^\circ}}$

$d_{p1} = 14.723$

The player 2 distance is:

$\frac{\sin{41^\circ}}{10} = \frac{\sin{64^\circ}}{d_{p2}}$

$d_{p2} = \frac{10\sin{75^\circ}}{\sin{64^\circ}}$

$d_{p2} = 10.747$

The farthest distance is of 14.723 yards, as 14.723 > 10.747.

You can learn more about the law of sines at https://brainly.com/question/12827625