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

Non-right-angled triangles — practice question

The sketch locates four islands at $A$, $B$, $C$ and $D$. $A$ lies due north of $B$. $\angle DAC = 48^\circ$, $\angle CAB = 55^\circ$ and $\angle BCA = 51^\circ$. $AC = 19\text{ km}$ and $AD = 27\text{ km}$.
(a)[1]

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

(b)[1]

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

(c)[3]

Calculate the distance between $A$ and $B$.

(d)[3]

Calculate the distance between $D$ and $C$.

(e)[4]

A boat starts from $D$ and travels in a straight line to $A$ at constant speed. The journey from $D$ to $A$ takes $3$ hours and $36$ minutes. $X$ is the point on $DA$ that is nearest to $C$. Calculate the time, correct to the nearest minute, that the boat needs to travel from $D$ to $X$.

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