Mathematics 4024 · O Level · Right-angled triangles

Right-angled triangles — practice question

Ports $A$ and $B$ are $15\text{ km}$ apart, with $B$ lying directly south of $A$. A boat sets off from $A$ on a bearing of $141^\circ$.
(a)[1]

State the bearing of $A$ from the boat.

(b)[2]

Calculate the least distance between the boat and $B$.

(c)[2]

Find the boat’s distance from $A$ when it is due east of $B$.

(d(i))[2]

After travelling $24\text{ km}$, the boat arrives at point $X$. Label $X$ on the diagram.

(d(ii))[3]

A second boat is less than $12\text{ km}$ from $A$ and is closer to $BC$ than to $BA$. Shade the area where this second boat can be.

(d(iii))[2]

Point $Y$ is where the second boat is furthest from $X$. Mark and label $Y$ on the diagram, then use it to find the maximum possible distance between the two boats.

Worked solution & mark scheme

This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: The bearing is $321^\circ$.

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