## Exam-Style Questions on Trigonometry 3D## Problems on Trigonometry 3D adapted from questions set in previous Mathematics exams. |

## 1. | GCSE Higher |

Rectangle ABCD is the horizontal base of a trapezoidal prism ABCDEFGH.

EF is parallel to AB. BC = 20cm, DC = 150mm, GC = 74mm, HG = 86mm and AE = BF.

(a) Find the size of angle ABF.

(b) Show that FD = 242 mm correct to 3 significant figures.

## 2. | GCSE Higher |

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.

## 3. | IB Studies |

ABC is a triangular car park on horizontal ground. The length of AB is 90m and the length of AC is 65m. The size of angle BCA is 68^{o}.

(a) Find the size of angle ABC.

(b) Find the area of the triangular car park.

M is the midpoint of AC.

(c) Find the length of BM.

A vertical flag pole, FB, is erected in one corner of the car park with its base at B.

The angle of elevation of F from M is 55.3^{o}. H is the midpoint of the flag pole.

(d) Calculate the angle of elevation of H from M.

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