(i) Sketch a diagram to illustrate this information. Label the points ${\text{A, B, C}}$. Show the angles ${90^ \circ }$, ${60^ \circ }$ and the length $7.3{\text{ cm}}$ on your diagram.

(ii) Find the length of ${\text{BC}}$.

Point ${\text{D}}$ is on the straight line ${\text{AC}}$ extended and is such that angle ${\text{CDB}}$ is ${20^ \circ }$.

(i) Show the point ${\text{D}}$ and the angle ${20^ \circ }$ on your diagram.

(ii) Find the size of angle ${\text{CBD}}$.

Unit penalty (UP) is applicable where indicated in the left hand column.

(i)

     (A1)

For ${\text{A}}$, ${\text{B}}$, ${\text{C}}$, $7.3$, ${60^ \circ }$, ${90^ \circ }$, shown in correct places     (A1)

Note: The ${90^ \circ }$ should look like ${90^ \circ }$ (allow $\pm {10^ \circ }$)

(ii) Using $\tan 60$ or $\tan 30$     (M1)

(UP)     $4.21{\text{ cm}}$     (A1)(ft)

Note: (ft) on their diagram

Or

Using sine rule with their correct values     (M1)

(UP)     $= 4.21{\text{ cm}}$     (A1)(ft)

Or

Using special triangle $\frac{{7.3}}{{\sqrt 3 }}$     (M1)

(UP)     $4.21{\text{ cm}}$     (A1)(ft)

Or

Any other valid solution

Note: If A and B are swapped then ${\text{BC}} = 8.43{\text{ cm}}$     (C3)

[3 marks]

(i) For ${\text{ACD}}$ in a straight line and all joined up to ${\text{B}}$, for ${20^ \circ }$ shown in correct place and ${\text{D}}$ labelled. ${\text{D}}$ must be on ${\text{AC}}$ extended.     (A1)

(ii) ${\text{B}}\hat {\text{C}}{\text{D}} = {120^ \circ }$     (A1)

${\text{C}}\hat {\text{B}}{\text{D}} = {40^ \circ }$     (A1)     (C3)

[3 marks]

The initial diagram was well drawn by most candidates but few could extend ${\text{AC}}$ to find ${\text{D}}$. The point ${\text{D}}$ was either drawn between ${\text{A}}$ and ${\text{C}}$ or on ${\text{CA}}$ extended. When on ${\text{CA}}$ extended the candidates could be awarded A1 follow through for the angle. A surprising number of candidates could not find the correct answer for the length of ${\text{BC}}$.

The initial diagram was well drawn by most candidates but few could extend ${\text{AC}}$ to find ${\text{D}}$. The point ${\text{D}}$ was either drawn between ${\text{A}}$ and ${\text{C}}$ or on ${\text{CA}}$ extended. When on ${\text{CA}}$ extended the candidates could be awarded A1 follow through for the angle. A surprising number of candidates could not find the correct answer for the length of ${\text{BC}}$.