1. **State the problem:** We need to find the height $h$ at which the volleyball player hits the ball. The volleyball net is 8 feet tall, the ball lands 15 feet away from the base of the net, and the distance from the player's hit position to the ball's landing spot (the hypotenuse) is 20.825 feet. 2. **Identify the right triangle:** The vertical side of the triangle is the sum of the net height and the height $h$ where the ball is hit, so vertical side = $8 + h$ feet. The horizontal side is 15 feet. The hypotenuse is 20.825 feet. 3. **Use the Pythagorean theorem:** For a right triangle with legs $a$ and $b$ and hypotenuse $c$, the relation is: $$a^2 + b^2 = c^2$$ Here, $a = 8 + h$, $b = 15$, and $c = 20.825$. 4. **Set up the equation:** $$ (8 + h)^2 + 15^2 = 20.825^2 $$ 5. **Calculate known squares:** $$ 15^2 = 225 $$ $$ 20.825^2 = 433.757625 $$ 6. **Substitute and simplify:** $$ (8 + h)^2 + 225 = 433.757625 $$ $$ (8 + h)^2 = 433.757625 - 225 $$ $$ (8 + h)^2 = 208.757625 $$ 7. **Take the square root of both sides:** $$ 8 + h = \pm \sqrt{208.757625} $$ $$ 8 + h = \pm 14.45 $$ 8. **Solve for $h$:** - If $8 + h = 14.45$, then $h = 14.45 - 8 = 6.45$ feet. - If $8 + h = -14.45$, then $h = -14.45 - 8 = -22.45$ feet (not physically possible since height cannot be negative). 9. **Final answer:** The height of the ball when the player hits it is approximately **6.45 feet**.