Select the correct answer.
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 triangle with three edges a kicker, left post, and right post. A line is drawn from the vertex kicker to the base, named goalie. The distance between the kicker and left post is 13 yd, the left post and goalie is 4 yd, and the goalie and right is 5 yd.
 A. 
9 yards
 B. 
16 yards
 C. 
13 yards
 D. 
17 yards

To solve this problem, we can use the fact that the goalie bisects the angle at the kicker's position, meaning the segments from the goalie to the left post and the right post are proportional to the distances from the kicker to those posts.

Given:
- Distance from kicker to the left post (\( KL \)) = 13 yards
- Distance from the goalie to the left post (\( LG \)) = 4 yards
- Distance from the goalie to the right post (\( RG \)) = 5 yards

We need to find the distance from the kicker to the right post (\( KR \)).

By the Angle Bisector Theorem:

\[
\frac{KR}{KL} = \frac{RG}{LG}
\]

Substitute the given values:

\[
\frac{KR}{13} = \frac{5}{4}
\]

Now, solve for \( KR \):

\[
KR = 13 \times \frac{5}{4} = 13 \times 1.25 = 16.25 \text{ yards}
\]

Rounding to the nearest yard:

\[
KR \approx 16 \text{ yards}
\]

So, the correct answer is:

**B. 16 yards**

Would you like more details on the solution, or do you have any questions? Here are 5 related questions you might find interesting:
1. How does the Angle Bisector Theorem apply to other geometric problems?
2. Can you calculate the exact angle bisected by the goalie?
3. How does the Angle Bisector Theorem relate to other triangle properties?
4. What is the significance of the proportionality in the Angle Bisector Theorem?
5. How would the answer change if the goalie were closer to the right post?

**Tip:** The Angle Bisector Theorem is a handy tool in triangle problems, especially when dealing with distances and proportionality.

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 triangle with three edges: a kicker, left post, and right post. A line is drawn from the vertex kicker to the base, named goalie. The distance between the kicker and the left post is 13 yd, the left post and goalie is 4 yd, and the goalie and right post is 5 yd.

A. 9 yards
B. 16 yards
C. 13 yards
D. 17 yards

Explore how to solve a soccer free kick problem using the Angle Bisector Theorem. Learn to calculate the distance from the kicker to the right post when the goalie bisects the angle. This problem highlights key geometry concepts and is suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation