Question

the figure gives the dimensions, in inches (in), of a typical safety cone. what is the length of the slant height s, in in? (round your answer to the nearest tenth of an inch.)

Explanation:

Step1: Find the radius of the base

The diameter of the base is \(12\) in. The radius \(r=\frac{12}{2} = 6\) in.

Step2: Apply the Pythagorean theorem

The height of the cone - like part (using the relevant dimensions) forms a right - triangle with the radius and the slant height. Let the height of the right - triangle (from the center of the base to the top of the cone - like part) be \(h = 28\) in and \(r = 6\) in.
By the Pythagorean theorem \(s=\sqrt{r^{2}+h^{2}}\).
Substitute \(r = 6\) and \(h = 28\) into the formula: \(s=\sqrt{6^{2}+28^{2}}=\sqrt{36 + 784}=\sqrt{820}\).

Step3: Calculate the value

\(\sqrt{820}\approx28.6\)

Answer:

\(28.6\)