GCSE · Trigonometry (sine & cosine rules)

Area of a triangle & 3D trigonometryExam-style questions

Why ½ab sin C works for any triangle, using it in reverse to find an angle, and the method for 3D problems — find the right-angled triangle inside the solid, then work in two dimensions.

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14 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 3 Level 4 Level 5

1
The diagram shows a cuboid measuring $12$ cm by $5$ cm by $9$ cm.Diagram NOT accurately drawn

Work out the angle between the long diagonal of the cuboid and its base. Give your answer correct to 1 decimal place.
Level 5 · 3 marksTry it
2
The diagram shows a pyramid with a square base of side $10$ cm. Each sloping edge has length $13$ cm.Diagram NOT accurately drawn

(a) Work out the vertical height of the pyramid. Give your answer correct to 1 decimal place.

(b) Work out the angle between a sloping edge and the base. Give your answer correct to 1 decimal place.
Level 5 · 5 marksTry it
3
A pyramid has a square base of side $12$ cm and a vertical height of $8$ cm. The apex is directly above the centre of the base.

Work out the angle between a sloping edge and the base. Give your answer correct to 1 decimal place.
Level 5 · 3 marksTry it
4
A pyramid has a square base of side $8$ cm. The apex $V$ is directly above the centre of the base, at a height of $6$ cm.

(a) Work out the length of a sloping edge of the pyramid. Give your answer correct to 3 significant figures. [3]

(b) Work out the angle between a sloping edge and the base. Give your answer correct to 1 decimal place. [2]
Level 5 · 5 marksTry it
5
The diagram shows a cuboid $ABCDEFGH$ . $AC = 7.5$ cm $\qquad$ $AG = 15$ cm

Find the angle that the line $AG$ makes with the plane $ABCD$ .

(2 marks)
Level 5 · 2 marksTry it

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