19M.2.AHL.TZ2.H_1

pestleMathematicsAAHLPaper 219M· sl-3-2-2d-and-3d-trig-sine-rule-cosine-rule-areasource ↗

In triangle ABC, AB = 5, BC = 14 and AC = 11.

Find all the interior angles of the triangle. Give your answers in degrees to one decimal place.

Markscheme / solution

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

attempt to apply cosine rule M1

${\text{cos}}\,{\text{A}} = \frac{{{5^2} + {{11}^2} - {{14}^2}}}{{2 \times 5 \times 11}} = - 0.4545 \ldots$

$\Rightarrow {\text{A}} = 117.03569 \ldots ^\circ$

$\Rightarrow {\text{A}} = 117.0^\circ$ A1

attempt to apply sine rule or cosine rule: M1

$\frac{{{\text{sin}}\,117.03569 \ldots ^\circ }}{{14}} = \frac{{{\text{sin}}\,{\text{B}}}}{{11}}$

$\Rightarrow {\text{B}} = 44.4153 \ldots ^\circ$

$\Rightarrow {\text{B}} = 44.4^\circ$ A1

${\text{C}} = 180^\circ - {\text{A}} - {\text{B}}$

${\text{C}} = 18.5^\circ$ A1

Note: Candidates may attempt to find angles in any order of their choosing.

[5 marks]

Examiners’ report

[N/A]