The diagram indicates the locations of a port, $A$, and a lighthouse, $L$.
The circle with centre $L$ and radius 40 km marks the area from which the lighthouse’s light is visible.
The straight line, $ABCD$, is the route followed by a ship after it departs from the port.
At position $B$, the ship is directly west of the lighthouse.
$AL = 92.1\text{ km}$, $AB = 61.1\text{ km}$ and $BL = 40\text{ km}$.
(a)[4]
Use the cosine rule to establish that angle $ABL = 130.1^\circ$, accurate to 1 decimal place.
(b)[4]
Calculate the bearing from the port, $A$, to the lighthouse, $L$.
(c)[5]
Calculate how long the lighthouse light is visible from the ship. Give your answer to the nearest minute.
Worked solution & mark scheme
This 13-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Accurate cosine-rule expression used implicitly” …