Question

A regular hexagon is shown.

Answer 1

The central angle of the hexagon is equal to 60º.

Therefore, the trigonometric relationship for the radius is given by:

$cos (30) = \frac{a}{c}$

Where,

a: apothema of the hexagon

c: Hexagon radius.

Clearing the radio we have:

$c = \frac{a}{cos (30)}$

Substituting values:

$c = \frac{12}{cos (30)} c = 13.85$

Rounding to the nearest whole number we have:

$c = 14 in$

Answer:

The measure of the radius, c, rounded to the nearest inch is:

C. 14 in.

Answer 2

The measure of the radius, c, rounded to the nearest inch is C. 14 in.

Further explanation

A regular hexagon is shown.  Hexagon is a six-sided polygon or 6-gon. The total of the internal angles of hexagon is 720°. The two-dimensional shape has 6 sides: 6 vertices and 6 angles. We can find the shape of a hexagon in a honeycomb and a football etc. A hexagon is an example of a polygon, or a shape with many sides. The hexagon is the strongest shape known because hexagonal patterns are prevalent in nature due to their efficiency.

What is the measure of the radius, c, rounded to the nearest inch? Use the appropriate trigonometric ratio to solve.

The central angle = 60º.

So the trigonometric relationship for the radius is:

$cos30 = \frac{a}{c}$

Where,

$a$ is apothema of the hexagon, $c$ is hexagon radius.

By clearing the radio, we have:

$c = \frac{a}{cos30}$

Then by substituting values:

$c = \frac{12}{cos30} = 13.85$

By rounding to the nearest whole number we have:

$c = 14 inch$

Learn more

1. Learn more about radius brainly.com/question/9467934
2. Learn more about inch brainly.com/question/384608
3. Learn more about hexagon brainly.com/question/11977772

Answer details

Grade:  9

Subject:  mathematics

Chapter:  hexagon

Keywords: inch,  radius, hexagon, trigonometric, ratio