I need help on a proportionality and similar triangle question

Question

A tennis player stands 39 feet behind the net, which is 3.5 feet tall. He extends his racket to a height of 9 feet and hits a serve. The ball passes 6 inches above the net. How far beyond the net does the tennis ball strike the court? Suggestion: If d is the distance past the net, the distance from the server to where the ball strikes is 39 + d.

Answer 1

Known:

• Player is standing 39 feet from the net.
• The net is 3.5 feet tall.
• The ball is hit from 9 feet in the air.
• The ball passes 6 inches (or half a foot) over the net

We can add the height of the net and the height of the ball as it passes over the net to get a height of 4 feet.

 

We draw a diagram. The height is 9 feet, vertical. We draw a horizontal line at the base of the vertical that is 39 feet long. We draw a vertical line that is 4 feet high from the end of this line. We draw a diagonal line from the top of the 9 foot line, passing through the top of the four foot line and ending on the (extended) line we drew earlier. This gives us to similar right triangles.

 

The first triangle has a height of 9 feet and a length of (39 + x) feet. The second triangle has a height of 4 feet and a length of x feet.

 

 

The proportion is

 

9 / 39+x = 4 / x  -We cross multiply.

4(39+x) = 9x      -Simplify

156 + 4x = 9x     -Subtract 4x from both sides

156 = 5x             -Divide both sides of equation by 5

31.2 = x

x = 31.2 feet