Question

find the height of this cone using the pythagorean theorem. pythagorean theorem: a² + b² = c²

Explanation:

Step1: Identify the values for Pythagorean Theorem

Let the radius of the cone base $b = 6$ in and the slant - height $c=9$ in. We want to find the height $a = h$.

Step2: Rearrange the Pythagorean Theorem

From $a^{2}+b^{2}=c^{2}$, we can solve for $a$: $a=\sqrt{c^{2}-b^{2}}$.

Step3: Substitute the values

Substitute $b = 6$ and $c = 9$ into the formula: $h=\sqrt{9^{2}-6^{2}}=\sqrt{81 - 36}=\sqrt{45}$ in.

Answer:

$\sqrt{45}$