Question

find h. hint: enter the number that belongs under the radical.

Explanation:

Step1: Identify right - triangle sides

The slant height of the cone is the hypotenuse ($c = 13$ cm) and the radius of the base is one of the legs ($a=\frac{8}{2}=4$ cm). We want to find the height $h$ (the other leg, let's call it $b$).

Step2: Apply Pythagorean theorem

Using $a^{2}+b^{2}=c^{2}$, substitute $a = 4$ and $c = 13$. So, $4^{2}+b^{2}=13^{2}$, which simplifies to $16 + b^{2}=169$.

Step3: Solve for $b^{2}$

Subtract 16 from both sides of the equation: $b^{2}=169 - 16=153$.

Answer:

153