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

Non-right-angled triangles — practice question

The diagram indicates the locations of three farms $A$, $B$ and $C$ on level ground. Farm $B$ lies on a bearing of $125^{\circ}$ from farm $A$. $AB = 950\,\text{m}$, $BC = 680\,\text{m}$ and $AC = 520\,\text{m}$.
(a)[3]

Show that $\angle BAC = 44.0^{\circ}$, to 1 decimal place.

(b)[1]

Calculate the bearing of $A$ from $C$.

(c)[4]

Farms $A$ and $B$ are linked by the straight track $AB$. Amira walks along the track from $A$ at a steady speed of $4.6\,\text{km/h}$. Calculate the time needed for Amira to walk from $A$ to the point nearest to farm $C$. Give your answer in minutes and seconds, correct to the nearest second.

(d)[4]

A helicopter is positioned vertically above farm $B$. The angle of elevation to the helicopter from farm $A$ is $10.7^{\circ}$. Calculate the angle of elevation of the helicopter from farm $C$.

Worked solution & mark scheme

This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: Apply cosine rule

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