Question

a free kick is given in a soccer game where the player taking the kick is 13 yards from the left post. the goalie is standing on the goal line at a point where he is 4 yards from the left post and 5 yards from the right post, to be sure that the angle that the kicker can kick and score is bisected. how far is the kicker from the right post, to the nearest yard?

a. 13 yards
b. 16 yards
c. 17 yards
d. 9 yards

Explanation:

Step1: Use the Angle - Bisector Theorem

The Angle - Bisector Theorem states that if a ray bisects an angle of a triangle, then it divides the opposite side into segments proportional to the other two sides. Let the length from the kicker to the right post be \(y\). We have \(\frac{4}{5}=\frac{13}{y}\).

Step2: Solve the proportion for \(y\)

Cross - multiply: \(4y = 5\times13\). So \(4y=65\), then \(y=\frac{65}{4}=16.25\approx16\) (rounded to the nearest yard).

Answer:

B. 16 yards