| Date | May 2018 | Marks available | 3 | Reference code | 18M.1.sl.TZ2.8 |
| Level | SL only | Paper | 1 | Time zone | TZ2 |
| Command term | Calculate | Question number | 8 | Adapted from | N/A |
Question
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]
a.
Calculate the area of the park.
[3]
b.
Markscheme
(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]
a.
\(\frac{1}{2}\) × 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]
b.
Examiners report
[N/A]
a.
[N/A]
b.
Syllabus sections
Topic 5 - Geometry and trigonometry » 5.3 » Use of the sine rule: \(\frac{a}{{\sin A}} = \frac{b}{{\sin B}} = \frac{c}{{\sin C}}\).
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