Question

Emma is playing miniature golf. Her ball is 2 feet to the left of the right-hand wall. The hole is 4 feet to the left of the wall. The distance along the wall between her ball and the hole is 18 feet. There is an obstacle between her ball and the hole, so Emma must hit her ball off the right-hand wall to reflect it towards the hole. How far down the wall should she aim?

Answer 1

Emma should aim 9 feet down the wall.

Step-by-step explanation:

To calculate the distance down the wall that Emma should aim, we need to use the concept of reflection and the properties of right angles. Since the ball is 2 feet to the left of the right-hand wall, and the hole is 4 feet to the left of the wall, the distance between the ball and the hole along the wall is 18 feet. To reflect the ball off the wall towards the hole, Emma should aim halfway between the ball and the hole along the wall, which would be 9 feet down the wall.

Answer 2

• She should aim 6 feet down the wall

Step-by-step explanation:

The diagram attached sketches the situtation.

Since the angle with which the ball hits the wall is the same with which it bounces, angle β is the same for the two shown triangles.

Then, since both are right triangles, then all the angles are congruent and the triangles are similar. Hence, you can equal the ratios of the sides, to make an equation:

• x/4 = y/2 ⇒ x = 2y

You have other equation:

• x+ y = 18

Substitute

• 2y + y = 18
• 3y = 18
• y = 18/3
• y = 6 ← this is the distance down the wall where the ball should hit

• x = 2(6) = 12

Then, she should aim 6 feet down the wall.