AMO 2025 Junior College (Grade 11–12) Question 5

Question 5

A rectangular prism has a $2\times2$ square base and vertical-face diagonals of length 3. The angle $\alpha$ is between the two adjacent-face diagonals meeting at a vertex, as shown. Find $\tan\alpha$.

Question illustration

$\frac{\sqrt{14}}2$
$\frac{\sqrt{14}}5$
$\frac{2\sqrt{14}}5$
$\frac{2\sqrt{14}}3$