Question

Find the distance between vertices A and C of a regular hexagon whose sides are 20 cm each angle of the hexagon is 120 degrees

Answer 1

Use cosine law to find b:

$b^2=a^2+b^2-2ac*cosB$$\begin{gathered} b^2=(20cm)^2+(20cm)^2-2(20cm)(20cm)*cos120º \\ b^2=400cm^2+400cm^2-800cm^2*(-0.5) \\ b^2=400cm^2+400cm^2+400cm^2 \\ b^2=1200cm^2 \\ b=\sqrt{1200cm^2} \\ b=20\sqrt{3}cm \\ b\approx34.64cm \end{gathered}$

Then, the distance between A and C is 20√3 cm or approximately 34.64 cm