21M.1.SL.TZ1.9

pestleMathematicsAISLPaper 121M· sl-3-2-2d-and-3d-trigsource ↗

A triangular field $ABC$ is such that $AB = 56 m$ and $BC = 82 m$ , each measured correct to the nearest metre, and the angle at $B$ is equal to $105 °$ , measured correct to the nearest $5 °$ .

Calculate the maximum possible area of the field.

Markscheme / solution

attempt to find any relevant maximum value (M1)

largest sides are $56.5$ and $82.5$ (A1)

smallest possible angle is $102.5$ (A1)

attempt to substitute into area of a triangle formula (M1)

$\frac{1}{2} \times 56.5 \times 82.5 \times \sin (102.5 °)$

$= 2280 (m^{2}) (2275.37 \dots)$ A1

[5 marks]

Examiners’ report

[N/A]