Review question

# Can we find the lengths and angles in this pyramid? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R6589

## Question

An equilateral triangle $ABC$ has side length $6$ units. The three altitudes of the triangle meet at $N$. Show that $AN=2\sqrt{3}$ units.

This triangle is the base of a pyramid whose apex $V$ lies on the line through $N$ perpendicular to the plane $ABC$. Given that $VN=2$ units, prove that $\widehat{VAN}=30^\circ.$

The perpendicular from $A$ to the edge $VC$ meets $CV$ produced at $R$. Prove that $AR=\frac{3}{2}\sqrt{7}$ units, and find the exact value of $\cos \widehat{ARB}$.