Your friend is hitting a golf ball toward the hole.The line from your friend to the hole bisects the angleformed by the lines from your friend to the oak treeand from your friend to the sand trap. The oak tree is250 yards from him. The sand trap is 375 yards fromhim. The hole is 225 yards from the sand trap. How faris the hole from the oak tree?

Question

ZofiaL279013 ZofiaL279013

28-10-2022
Mathematics

contestada

Your friend is hitting a golf ball toward the hole.The line from your friend to the hole bisects the angleformed by the lines from your friend to the oak treeand from your friend to the sand trap. The oak tree is250 yards from him. The sand trap is 375 yards fromhim. The hole is 225 yards from the sand trap. How faris the hole from the oak tree?

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ZeelV670826 ZeelV670826 · Answer 1 · 2022-10-28T10:22:38+02:00

Solution:

Given:

Since the line from your friend to the hole bisects the angle formed by the lines from your friend to the oak tree and from your friend to the sand trap, then the angles are the same.

Using the angle bisector theorem of a triangle which states that if a ray bisects an angle in a triangle, then it divides the opposite sides of the triangle into segments that are proportional to the other two sides.

This is as shown below;

Hence, applying the angle bisector theorem,

[tex]\begin{gathered} \frac{250}{375}=\frac{x}{225} \\ \text{Cross multiplying,} \\ 375x=250\times225 \\ 375x=56250 \\ \text{Dividing both sides by 375,} \\ x=\frac{56250}{375} \\ x=150yd \end{gathered}[/tex]

Therefore, the hole from the oak tree is 150yd apart.