21N.2.SL.TZ0.3

EITHER

attempt to use cosine rule               (M1)

${12}^2+{\mathrm{AB}}^2-2\times 12\times \cos 25°\times \mathrm{AB}=7^2$  OR  ${\text{AB}}^2-21.7513\dots \text{AB}+95=0$                 (A1)

at least one correct value for $\mathrm{AB}$                 (A1)

$\mathrm{AB}=6.05068\dots$  OR  $\mathrm{AB}=15.7007\dots$

using their smaller value for $\mathrm{AB}$ to find minimum perimeter               (M1)

$12+7+6.05068\dots$

OR

attempt to use sine rule               (M1)

$\frac{\sin \text{B}}{12}=\frac{{\displaystyle \sin 25°}}{{\displaystyle 7}}$  OR  $\sin \text{B}=0.724488\dots$  OR  $\hat{\text{B}}=133.573\dots °$  OR  $\hat{\text{B}}=46.4263\dots °$                 (A1)

at least one correct value for $C$                 (A1)

$\hat{C}=21.4263\dots °$  OR  $\hat{C}=108.573\dots °$

using their acute value for $\hat{C}$ to find minimum perimeter               (M1)

$12+7+\sqrt{{12}^2+7^2-2\times 12\times 7 \cos 21.4263\dots °}$  OR  $12+7+\frac{7 \sin 21.4263\dots °}{\sin 25°}$

THEN

$25.0506\dots$

minimum perimeter $=25.1$.                       A1

 

[5 marks]

[N/A]