The diagram shows a right-angled triangular prism ABCDEF - OCR - GCSE Maths - Question 18 - 2019 - Paper 4

To find angle FDC, we can use the tangent function:

$\tan(FDC) = \frac{CD}{CF} = \frac{10}{6}$

Calculating this gives:

$FDC = \tan^{-1}\left(\frac{10}{6}\right) \approx 30.96°$

Rounding to the nearest degree, we find:

$FDC \approx 31°$

To find the length of AF, we can use the Pythagorean theorem in triangle ACD:

Let AC be the length we need to find. Then:

$AC^2 = AD^2 + CD^2$

Substituting the known values:

$AC^2 = 11^2 + 10^2 = 121 + 100 = 221$

So,

$AC = \sqrt{221}$

Thus, the length of AF is:

$AF = AC + CF = \sqrt{221} + 6$

Calculating this gives:

$AF = 14.8 \, \text{cm} ext{ (approximately)}$