- 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