A-level · Trigonometry

The sine and cosine rulesExam-style questions

Solving any (non-right-angled) triangle — the sine rule, the cosine rule and the area formula ½ab·sinC — and how to choose the right one from what you're given.

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15 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4

1
In the triangle $DEF$ , $DE = 10$ cm, $DF = 16$ cm and angle $EDF = \theta°$ .

The area of triangle $DEF$ is $56$ cm².
(a) Find the exact value of $\sin \theta°$ .

(2 marks)

Given that angle $EDF$ is obtuse,
(b) find the length of $EF$ , giving your answer in cm to 3 significant figures.

(3 marks)
Level 3 · 5 marksTry it
2
In triangle $ABC$ , angle $A = 35^\circ$ , $a = 7$ and $b = 10$ . Show that there are two possible triangles, and find both possible values of angle $B$ , to 1 decimal place.
Level 3 · 4 marksTry it
3
In triangle $ABC$ , $AB = 8$ cm, angle $BAC = 40^\circ$ and angle $ABC = 75^\circ$ . Find
(a) angle $ACB$ ,
(b) the length $BC$ , and (c) the area of the triangle, to 3 significant figures.
Level 3 · 6 marksTry it
4
In triangle $ABC$ , $b = 9$ cm, $c = 11$ cm and angle $A = 120^{\circ}$ .

Find $a$ , giving your answer to $3$ significant figures. (3 marks)
Level 3 · 3 marksTry it
5
A triangle has sides of length $5$ cm, $6$ cm and $9$ cm.

Find the largest angle of the triangle, giving your answer to $1$ decimal place. (4 marks)
Level 3 · 4 marksTry it

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