Question

Imagine two line segments where each represents a slant height of the cone. The segments are on opposite sides of the cone and meet at the apex. Find the measurement of the angle formed between the line segments.

Answer 1

To determine the slant height of the cone, we will apply the Pythagorean theorem to the right triangle ABC.

From the Pythagorean theorem we get that:

`AC^2=AB^2+BC^2.`

We are given that:

`\begin{gathered} BC=6in, \\ AB=(4in)/(2)=2in. \end{gathered}`

Therefore:

`AC^2=(6in)^2+(2in)^2=36in^2+4in^2.`

Finally, solving for AC, we get:

`AC=√(40in^2)=2√(10)\text{ in.}`

Answer:

`\begin{equation*} 2√(10)\text{ in.} \end{equation*}`