Review question

# Using angles in a pentagon... Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R7021

## Question

$ABCDE$ is a regular pentagon. By projecting the broken line $AED$ on the line $AB$, or otherwise, show that $\cos\dfrac{\pi}{5}-\cos\dfrac{2\pi}{5}=\frac{1}{2}.$

Hence, or otherwise, show that $\cos\dfrac{\pi}{5} = \dfrac{\sqrt{5}+1}{4}$.

Show further that $\cos\dfrac{3\pi}{5} = -\dfrac{\sqrt{5}-1}{4}$.