Question

find h. first we must set up our equation using the pythagorean theorem a² + b² = c² 4² + b² = 13² 16 + b² = 169 b² = 153 b = √? 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 side ($a=\frac{8}{2}=4$ cm). We use the Pythagorean theorem $a^{2}+b^{2}=c^{2}$ to find the height $h$ (represented as $b$ here).

Step2: Substitute values into Pythagorean theorem

$4^{2}+b^{2}=13^{2}$. Calculate $4^{2}=16$ and $13^{2}=169$. So, $16 + b^{2}=169$.

Step3: Solve for $b^{2}$

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

Answer:

153