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
A triangle has two sides of length $11$ cm and $14$ cm, and an area of $42$ cm².

The angle between the two given sides is acute.

Work out the size of this angle. Give your answer correct to 1 decimal place.
Level 4 · 3 marksTry it
2
A triangular field has two sides of length $8$ m and $15$ m, with an angle of $70°$ between them.

(a) Work out the area of the field. Give your answer correct to 1 decimal place.

(b) Work out the length of the third side. Give your answer correct to 1 decimal place.
Level 4 · 5 marksTry it
3
A triangle has two sides of length $8$ cm and $10$ cm, and an area of $30$ cm $^2$ .

The angle between the two given sides is acute.

Work out the size of this angle. Give your answer correct to 1 decimal place.
Level 4 · 3 marksTry it
4
A cuboid measures $8$ cm by $6$ cm by $5$ cm.

Work out the length of the longest diagonal of the cuboid. Give your answer correct to 3 significant figures.
Level 4 · 3 marksTry it
5
A cuboid measures $8$ cm by $6$ cm by $5$ cm.

Work out the angle between the longest diagonal of the cuboid and the base. Give your answer correct to 1 decimal place.
Level 4 · 3 marksTry it

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