## Exam-Style Question on Trigonometry 3D## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 526. This question is similar to one that appeared on a GCSE Higher paper in 2019. The use of a calculator is allowed.

A triangular prism is made using two right-angled triangles and three rectangular pieces of cardboard. Five of the vertices have been labeled \(A, B, C, D \text{ and } E\) as shown in the photograph below.

$$ AB = 17cm, \quad BC = 24cm, \quad DC = 28cm $$

Imagine a point \(F\) on the line \(DC\) such that:

$$ DF : FC = 3 : 4 $$Calculate the size of the angle between \(AF\) and the base of the prism.

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