Find the number of units in the length of diagonal DA of the regular hexagon shown. Express your answer in simplest radical form.

Guest May 29, 2018

#1**+2 **

For a polygon, the SUM of the internal angles is (n-2) * 180 (n=6 for hexagon)

(6-2)*180 = 720 Thus EACH angle is : 720/6 = 120 degrees

So the large angle of the triangle is 120 degrees the other two are equal to each other

there are 180 degrees in any triangle:

(180-120) / 2 = 30 degrees for each of the smaller angles.

Now use the law of sines

10/sin30 = x/(sin120)

10/(.5) * (sqrt3 )/ 2 = x

10 sqrt 3

10/sin30 * sin 120 = 17.32

ElectricPavlov
May 29, 2018

#2**+2 **

I already drew a diagram, but don't know how to upload it from my computer.

First you connect the point A to the two points that construct the line segment labeled 10.

AD is congruent to the line segment perpendicular to the side labelled 10.

You have constructed a 30 - 60 - 90 triangle. The hypotenuse is 20.

The leg is the square root of 20^2 - 10^2.

Can someone tell me how to upload an image, then this solution would be much clearer.

Thanks

GYanggg
May 29, 2018