The sketch depicts quadrilateral $ABCD$. Also, $AC = 12.3$ cm and $AD = 16.5$ cm. In addition, angle $BAC = 31^\circ$, angle $ABC = 90^\circ$ and angle $ACD = 90^\circ$.
(a)[2]
Show that $AB = 10.54$ cm, rounded to 2 decimal places.
(b)[2]
Show that angle $DAC = 41.80^\circ$, rounded to 2 decimal places.
(c)[3]
Calculate the length of $BD$.
(d)[4]
Calculate the value of angle $CBD$.
(e)[4]
Calculate the perpendicular distance from $C$ to $BD$.
Worked solution & mark scheme
This 15-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Hence, $\cos31^{\circ}=\dfrac{12.3}{AB}$” …