The true bearing from P to Q is \({194^o}\). What is the compass bearing from Q to P?

From A a ship sails for 4 Km on a bearing of \({045^o}\). At B the ship changes direction and sails for 3 Km on a bearing of \({165^o}\) to C.

Find the exact distance AC.

From a ship S sailing due north the bearing of a lighthouse L is \({040^o}\). After the ship has sailed 20 Km the bearing of L from the ship is \({150^o}\). Find the shortest distance that the ship is from the lighthouse.

(Give your answer to 1 decimal place)

Ship \(X\) is 30 nautical miles from port \(P\) and is on a bearing of \(065^\circ\). Ship \(Y\) is 40 nautical miles from port \(P\) and is on a bearing of \(125^\circ\).

i) Show that \(\angle XPY = 60^\circ\).

ii) Use the cosine rule to determine the distance between the two ships, giving your answer to one decimal place.

iii) Determine the bearing of ship \(X\) from the ship \(Y\), giving your answer to the nearest degree.

\(A\) is 14.6 km due east of \(O\). The bearings of \(B\) from \(O\) and \(A\) are \(048^\circ\) and \(028^\circ\) respectively.

i) Calculate the bearing of \(A\) from \(B\).

ii) Find the distance from \(A\) to \(B\), to three significant figures.

A ship travels from Port A for 6 nm on a bearing of \({\rm{030}}^\circ \) to Port B. It then turns and travels 5 nm to Port C on a bearing of \({\rm{120}}^\circ \). Find the distance AC.

Towns \(A, B\) and \(C\) are to be connected by high-speed optic fibre cables. Town \(B\) is due west of town \(A\). Town \(C\) is on a bearing of \(210^{\circ}\) from Town \(A\).

i) Find the size of \(\angle B A C\).

ii) Find the distance, to the nearest kilometre, between towns \(B\) and \(C\).

What is the bearing of point \(P\) from \(O\)?

The bearing angle of point B from point A is \({\rm{66}}^\circ \). Find the bearing angle of point A from point B.

A plane is 120 miles north and 85 miles east of an airport. If the pilot wants to fly directly to the airport, what bearing should be taken?

A boat sails from a certain port in the direction of \(S\)\({\rm{30}}^\circ \)\(E\). After the boat has sailed 8 km, how far is due east from the port?

A boat leaves from point S on a bearing of \({\rm{060}}^\circ \). After the boat has sailed 12 km, it reaches point P. How far is point P due east of point S?