Emma is playing miniature golf. Her ball is 2 feet of the right-wall. The hole is 4 feet to the left of the wall. The distance along the wall between her ballet and the hole is 18 feet. There is an obstacle between 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?

She should aim 6 feet down the wall

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.