Calculate the size of angle ACB.

Nadia makes an accurate drawing of triangle ABC. She measures angle BAC and finds it to be 29°.

Calculate the percentage error in Nadia’s measurement of angle BAC.

$\frac{{\sin {\text{A}}{\operatorname{\hat B}}{\text{C}}}}{{13.4}} = \frac{{\sin 30^\circ }}{{6.7}}$     (M1)(A1)

Note: Award (M1) for correct substituted formula, (A1) for correct substitution.

${\text{A}}{\operatorname{\hat B}}{\text{C}}$ = 90°     (A1)

${\text{A}}{\operatorname{\hat C}}{\text{B}}$ = 60°     (A1)(ft)     (C4)

Note: Radians give no solution, award maximum (M1)(A1)(A0).

[4 marks]

$\frac{{29 - 30}}{{30}} \times 100$     (M1)

Note: Award (M1) for correct substitution into correct formula.

% error = −33.3 %     (A1)     (C2)

Notes: Percentage symbol not required. Accept positive answer.

[2 marks]

Use of cosine rule was common. The assumption of a right angle in the given diagram was minimal.

The incorrect denominator was often seen in the error formula.