Answer:
18 inches
Step-by-step explanation:
To find how high the ball is before it begins to roll down the incline plane, we can model the given scenario as a right triangle, where:
- The hypotenuse represents the incline plane and distance the ball rolls from the top of the incline to the bottom (30 inches).
- The base of the triangle represents the width of the incline (24 inches).
To find the height of the right triangle, we can use the Pythagorean Theorem:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Pythagorean Theorem}}\\\\a^2+b^2=c^2\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$a$ and $b$ are the legs of the right triangle.}\\\phantom{ww}\bullet\;\textsf{$c$ is the hypotenuse (longest side) of the right triangle.}\\\end{array}}[/tex]
In this case:
- a = 24 inches
- b = height (h)
- c = 30 inches
Substitute the values into the formula and solve for h:
[tex]24^2+h^2=30^2\\\\576+h^2=900\\\\h^2=900-576\\\\h^2=324\\\\h=\sqrt{324}\\\\h=18[/tex]
Therefore, the height of the ball before it begins to roll down the incline plane is:
[tex]\LARGE\boxed{\boxed{18\; \rm inches}}[/tex]
