Mathematics 4024 · O Level · Right-angled triangles

Right-angled triangles — practice question

A boat departs from $A$ and covers $12\text{ km}$ to reach $B$.
(a)[2]

The boat departs from $A$ at $10\ 25$ and moves with an average speed of $15\text{ km/h}$. At what time will the boat reach $B$?

(b)[4]

The bearing of $B$ from $A$ is $056^\circ$. $B$ lies $2\text{ km}$ due west of $C$. Calculate $AC$.

(c)[2]

Point $C$ is at the foot of the cliff. Point $D$, the top of the cliff, is vertically above $C$. $DC$ is perpendicular to $BC$ and $DC = 105\text{ m}$. Calculate the angle of elevation of $D$ from $B$.

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