18M.1.SL.TZ2.T_8

pestleMathematicsAASLPaper 118M· sl-3-2-2d-and-3d-trig-sine-rule-cosine-rule-areasource ↗

A park in the form of a triangle, ABC, is shown in the following diagram. AB is 79 km and BC is 62 km. Angle A $\mathop {\text{B}}\limits^ \wedge$ C is 52°.

Calculate the length of side AC in km.

[3]

Calculate the area of the park.

[3]

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

(AC² =) 62² + 79² − 2 × 62 × 79 × cos(52°) (M1)(A1)

Note: Award (M1) for substituting in the cosine rule formula, (A1) for correct substitution.

63.7 (63.6708…) (km) (A1) (C3)

[3 marks]

$\frac{1}{2}$ × 62 × 79 × sin(52°) (M1)(A1)

Note: Award (M1) for substituting in the area of triangle formula, (A1) for correct substitution.

1930 km² (1929.83…km²) (A1) (C3)

[3 marks]

Examiners’ report

[N/A]