Points \(A,B\) and \(C\) are on horizontal ground.
\(AB=418\text{ m}\) and \(AC=680\text{ m}\).
\(B\) is on a bearing of \(312^\circ\) from \(A\).
\(C\) is due west of \(A\).
Show that \(BC=463.3\text{ m}\), correct to one decimal place.[2]
A surveyor is standing at point \(A\) and operates a drone hovering vertically above point \(C\).
The surveyor’s eye level is 1.74 m above the ground.
The angle of elevation of the drone from the surveyor’s eye level is \(16.5^\circ\).
Estimate the height of the drone above the ground at point \(C\).
Give your answer to one decimal place.[2]
The surveyor receives the following instructions.
Maintaining the same height above the ground, navigate the drone to a point \(T\) within triangle \(ABC\) such that \(T\) is equidistant from points \(B\) and \(C\), and is also equidistant from the lines \(AC\) and \(BC\).
Using geometrical constructions, locate and label point \(T\) on the diagram above.[3]
The surveyor receives further clarification about the location of \(T\).
\(T\) is on a bearing of \(x^\circ\) from \(C\).
\(CT=y\text{ m}\).
By calculation, find the values of \(x\) and \(y\).
Do not obtain your answers by measurement from the diagram.[5]