SPM.1.SL.TZ0.1

pestleMathematicsAASLPaper 1SPM· sl-3-2-2d-and-3d-trig-sine-rule-cosine-rule-areasource ↗

The following diagram shows triangle ABC, with AB = 6 and AC = 8.

Given that ${\text{cos}}\,\hat A = \frac{5}{6}$ find the value of ${\text{sin}}\,\hat A$ .

[3]

Find the area of triangle ABC.

[2]

Markscheme / solution

valid approach using Pythagorean identity (M1)

${\text{si}}{{\text{n}}^2}\,A + {\left( {\frac{5}{6}} \right)^2} = 1$ (or equivalent) (A1)

${\text{sin}}\,A = \frac{{\sqrt {11} }}{6}$ A1

[3 marks]

$\frac{1}{2} \times 8 \times 6 \times \frac{{\sqrt {11} }}{6}$ (or equivalent) (A1)

area $= 4\sqrt {11}$ A1

[2 marks]

Examiners’ report

[N/A]