the value of $\theta$.

the time at which the interception occurs, correct to the nearest minute.

let the interception occur at the point P, t hrs after 12:00

then, SP = 20t and MP = 30t     A1

using the sine rule,

$\frac{{{\text{SP}}}}{{{\text{MP}}}} = \frac{2}{3} = \frac{{\sin \theta }}{{\sin 135}}$     M1A1

whence $\theta = 28.1$     A1

[4 marks]

using the sine rule again,

$\frac{{{\text{MP}}}}{{{\text{MS}}}} = \frac{{\sin 135}}{{\sin (45 - 28.1255 \ldots )}}$     M1A1

$30t = 10 \times \frac{{\sin 135}}{{\sin 16.8745 \ldots }}$     M1

$t = 0.81199 \ldots$     A1

the interception occurs at 12:49     A1

[5 marks]