The diagram shows a triangular prism - Edexcel - GCSE Maths - Question 20 - 2019 - Paper 2

To find EM, we first identify point M's coordinates in a 3D space. Assuming point A is at (0, 0, 0), the coordinates of M will be (0, 0, 6). Point E is directly above point A, so its coordinates are (0, 15, 0).

Using the distance formula:

$EM = \sqrt{(0 - 0)^2 + (15 - 0)^2 + (0 - 6)^2}$ $EM = \sqrt{0 + 225 + 36}$ $EM = \sqrt{261} \approx 16.155$

To find the angle θ between EM and the base (the plane defined by ABCD), we use the tangent function:

$\tan(θ) = \frac{height \, EM}{base \, AB}$

Here, the height EM is approximately 16.155 and the base AB is 15 cm:

$\tan(θ) = \frac{16.155}{15}$

To find the angle θ:

$$θ = \tan^{-1}\left(\frac{16.155}{15}\right) \approx \tan^{-1}(1.077)$

Calculating this gives: $θ \approx 47.7°$