Hello, jlefholtz!

I think your diagram is off . . .

A ball is served from the center of the basemline into the deuce court.

If the ball is hit 9 ft above the ground and travels in a straight line down the middle of the court,

and the net is 3 ft high, how far from the base of the net will the ball land if it just clears the top of the net?

Additional information: The court is 78 feet long. Code:

*
| *
| *
| *
9| | *
| 3| *
| | *
*-----------------*-----------------------*
: - - - 39 - - - : - - - - - x - - - - - :

From similar triangles, we have: .$\displaystyle \frac{x}{3} \:=\:\frac{x+39}{9} $

Solve for $\displaystyle x\!:\;\;9x \:=\:3(x+30) \quad\Rightarrow\quad 9x \:=\: 3x + 117 \quad\Rightarrow\quad 6x \:=\:117 $

Therefore: .$\displaystyle x \:=\:\frac{117}{6} \;=\;19.5\text{ feet}$