Mathematics 0580 · IGCSE · Non-right-angled triangles

Non-right-angled triangles — practice question

In the diagram, the locations of two lighthouses $A$ and $B$, a boat $C$ and a harbour $H$ are shown. $C$ lies due east of $B$.
(a)[1]

Find the harbour's bearing from boat $C$.

(b(i))[1]

Show that angle $CBH$ is $100^\circ$.

(b(ii))[3]

Show that $BH = 13.7$ km, rounded to 1 decimal place.

(c)[5]

Calculate the bearing of $A$ as seen from $B$.

(d(i))[4]

Calculate the time at which boat $C$ reaches the harbour. Give the time correct to the nearest minute.

(d(ii))[3]

Calculate the distance from boat $C$ to the harbour when boat $C$ is at its shortest distance from lighthouse $B$.

Worked solution & mark scheme

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