19M.1.SL.TZ1.T_10

pestleMathematicsAASLPaper 119M· sl-3-2-2d-and-3d-trig-sine-rule-cosine-rule-areasource ↗

Three airport runways intersect to form a triangle, ABC. The length of AB is 3.1 km, AC is 2.6 km, and BC is 2.4 km.

A company is hired to cut the grass that grows in triangle ABC, but they need to know the area.

Find the size, in degrees, of angle BÂC.

[3]

Find the area, in km², of triangle ABC.

[3]

Markscheme / solution

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

$\left( {\cos \,A = } \right)\,\,\frac{{{{2.6}^2} + {{3.1}^2} - {{2.4}^2}}}{{2\left( {2.6} \right)\left( {3.1} \right)}}$ (M1)(A1)

Note: Award (M1) for substituted cosine rule formula, (A1) for correct substitutions.

48.8° (48.8381…°) (A1) (C3)

[3 marks]

$\frac{1}{2} \times 2.6 \times 3.1 \times {\text{sin}}\left( {48.8381 \ldots ^\circ } \right)$ (M1)(A1)(ft)

Note: Award (M1) for substituted area of a triangle formula, (A1) for correct substitution.