Home / CIE iGCSE Maths E6.6 Pythagoras’ theorem and trigonometry in 3D Exam Style Practice Questions- Paper 2

CIE iGCSE Maths E6.6 Pythagoras’ theorem and trigonometry in 3D Exam Style Practice Questions- Paper 2

CIE iGCSE Maths E6.6 Pythagoras’ theorem and trigonometry in 3D Exam Style Practice Questions- Paper 2

IGCSE Mathematics(0580) Practice Questions Paper 2 - All Chapters
Question

The diagram shows a pyramid ABCDE.
The pyramid has a square horizontal base ABCD with side 5 cm.
The vertex E is vertically above the centre O of the base.
The height OE of the pyramid is 9 cm.

Calculate the angle that EC makes with the base ABCD.

▶️ Answer/Explanation
Solution

Ans: 68.6° or 68.55° to 68.56°

1. Find half-diagonal of base: $\frac{5\sqrt{2}}{2} ≈ 3.5355$ cm

2. This forms adjacent side, height (9 cm) is opposite side

3. Angle is $\tan^{-1}\left(\frac{9}{3.5355}\right)$

4. Calculate: $\tan^{-1}(2.5456) ≈ 68.55°$

Question

The diagram shows a pyramid VABCD with a rectangular base. V is vertically above M, the intersection of the diagonals AC and BD. AB = 12cm, BC = 10cm and VC = 14cm. 

Pyramid diagram
Calculate the angle that VC makes with the base ABCD.
▶️ Answer/Explanation
Answer: 56.1° or 56.09°…
1. Find diagonal AC: √(12² + 10²) = √244 ≈ 15.62cm
2. Half-diagonal CM = AC/2 ≈ 7.81cm
3. Angle = cos⁻¹(CM/VC) = cos⁻¹(7.81/14) ≈ 56.1°
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