a) State or imply $R = \sqrt {10} $

Use trig formulae to find $\alpha $

Obtain $\alpha  = {71.57^ \circ }$ with no errors seen

[Do not allow radians in this part. If the only trig error is a sign error in $\cos \left( {x - \alpha } \right)$ give M1A0]

b) Evaluate ${\cos ^{ - 1}}(2/\sqrt {10} )$ correctly to at least 1 d.p. $\left( {50.7684{ \ldots ^ \circ }} \right)$  (Allow ${50.7^ \circ }$ here)

Carry out an appropriate method to find a value of $2\theta $ in ${0^ \circ } \lt 2\theta  \lt {180^ \circ }$

Obtain an answer for $\theta $ in the given range, e.g. $\theta  = {61.2^ \circ }$

Use an appropriate method to find another value of $2\theta $ in the above range

Obtain second angle, e.g. $\theta  = {10.4^ \circ }$, and no others in the given range

[Ignore answers outside the given range.]