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 triangle with two sides of length $9.4$ cm and $12.7$ cm, and an angle of $58°$ between them.Diagram NOT accurately drawn

Work out the area of the triangle. Give your answer correct to 1 decimal place.
Level 3 · 2 marksTry it
2
A triangle has two sides of length $7.5$ cm and $9.2$ cm, and the angle between them is $41°$ .

Work out the area of the triangle. Give your answer correct to 3 significant figures.
Level 3 · 2 marksTry it
3
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
4
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
5
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

9 more questions on area of a triangle & 3d trigonometry

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