Just a cute geometry problem

Geometry Level pending

Let $[VABC]$ be a regular triangular pyramid. Height $VO$ is 4cm. The area of triangle $ABC$ is $27\sqrt3\text{ cm}^{2}$ .

Find tan[(AVB);(AVM)], where {M} is the middle of [BC].

√2/2 √3 √39/6 1

1 solution

Gabi Dobre
Mar 17, 2016

Personally, I think that the best part of the problem was finding the angle (∠BPM). If you do the math, the final result is √39/6.