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
Figure 1

Diagram NOT accurately drawn

Figure 1 shows the plan view of a triangular field $PQR$ $P QR$ .

The point $S$ $S$ lies on $QR$ $QR$ , and a straight fence $PS$ $P S$ divides the field into two parts.

Given that
- $PQ = 10$ m
- $QS = x$ m
- $PS = (x + 2)$ m
- angle $PQS = \theta°$
(a) show that

$\cos \theta° = \frac{24 - x}{5x}$

(2 marks)

Given also that
- $x = 7$
- angle $PRQ = 38°$
(b) find the area of the field, giving your answer in m² to one decimal place.

(5 marks)
Level 4 · 7 marksTry it