Mathematics 4024 · O Level · Non-right-angled triangles

Non-right-angled triangles — practice question

$ABCD$ forms a rectangular field. $C$ lies directly south of $A$. $AB = 450\,\text{m}$ and $BC = 210\,\text{m}$.
(a(i))[3]

Martha travels at an average speed of $5.2\,\text{km h}^{-1}$. Calculate the time Martha needs to complete one circuit of the field. Give your answer correct to the nearest minute.

(a(ii))[3]

Show that the bearing of $D$ from $A$ is $245^{\circ}$, accurate to $3$ significant figures.

(b)[5]

In triangle $PQR$, point $S$ lies on $PR$. $PS = 10.3\,\text{cm}$, $QR = 12.6\,\text{cm}$, $\angle QPS = 42^{\circ}$ and $\angle QRS = 35^{\circ}$. Calculate $QS$.

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