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Using SOH CAH TOA, we realize that this problem would require us to use the tan function where the ratio would be, or for this problem's data. Now that we have the apothem and one of the angles, we can use trig functions to solve for.

This means that the angle of interest in the triangle is actually. Keep in mind that the drawn triangle is actually bisecting the internal angle. This measure of is the measure of the entire angle. Where is the number of sides of the hexagon. In order to solve for, the first step is to solve for the measure of an internal angle of the hexagon.

Keep in mind that is actually half the length of one side of the regular hexagon. In the previous image, the side of interest has been labeled as. If the apothem is and the question requires us to solve for the length of one of the sides, the problem can be resolved through the use of right triangles and trig functions.Īs long as one angle and one side length is known for a right triangle, trig functions can be used to solve for a mystery side.

Perfect hexagon measurements