Mathematics 0580 · IGCSE · Non-right-angled triangles

Non-right-angled triangles — practice question

The figure depicts a triangular field, $ABC$, laid out on level ground. An arrow indicates north. The side lengths are $AB = 120\text{ m}$, $AC = 150\text{ m}$ and $BC = 180\text{ m}$. The diagram is NOT TO SCALE.
(a)[3]

Olav travels from $A$ to $B$ at a steady speed of $4\text{ m/s}$ and then from $B$ to $C$ at a steady speed of $3\text{ m/s}$. He then travels from $C$ to $A$ at a constant speed. His average speed over the complete trip is $3.6\text{ m/s}$. Calculate his speed when he travels from $C$ to $A$.

(b)[4]

Use the cosine rule to determine angle $BAC$.

(c(i))[1]

Determine the bearing of $B$ from $A$.

(c(ii))[2]

Determine the bearing of $A$ from $B$.

(d)[2]

$D$ is the point on $AC$ closest to $B$. Calculate the distance from $D$ to $A$.

Worked solution & mark scheme

This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: Accurate total time calculation

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