Chapter 10

A ship travels for \(10 \mathrm{~km}\) on a bearing of \(30^{\circ} .\) It then follows a bearing of \(60^{\circ}\) for \(20 \mathrm{~km}\). Calculate the distance of the ship from the starting position.

For questions \(1-10\) solve \(\triangle \mathrm{ABC}\) given \(A=36^{\circ}, B=79^{\circ}, \mathrm{AC}=11.63 \mathrm{~cm}\)

In questions \(1-10\) solve \(\triangle \mathrm{ABC}\) given \(\mathrm{AB}=42 \mathrm{~cm}, \mathrm{BC}=37 \mathrm{~cm}, \mathrm{AC}=26 \mathrm{~cm}\)

In questions 1-11 \(\Delta \mathrm{ABC}\) has a right angle at \(\mathrm{C}\). Calculate \(\mathrm{AB}\) given \(\mathrm{AC}=9 \mathrm{~cm}\) and \(\mathrm{BC}=15 \mathrm{~cm}\)

Find the resultant of the forces shown in Figure \(5.14\). a. b.

In questions 1-11 \(\Delta \mathrm{ABC}\) has a right angle at \(\mathrm{C}\). Calculate \(\sin A\) given \(\mathrm{AC}=10 \mathrm{~cm}\) and \(\mathrm{AB}=14 \mathrm{~cm}\)

In questions \(1-10\) solve \(\triangle \mathrm{ABC}\) given \(\mathrm{AB}=29 \mathrm{~cm}, \mathrm{BC}=41 \mathrm{~cm}, B=100^{\circ}\)

An aeroplane flies 150 miles on a bearing of \(105^{\circ}\) and then 107 miles on a bearing of \(217^{\circ}\). Find the bearing that the aeroplane must take to fly directly back to the starting position.

For questions \(1-10\) solve \(\triangle \mathrm{ABC}\) given \(\mathrm{AB}=15 \mathrm{~cm}, \mathrm{AC}=23 \mathrm{~cm}, B=57^{\circ}\)

A ship travels \(50 \mathrm{~km}\) from \(\mathrm{O}\) on a bearing of \(290^{\circ}\) to get to position A. From A it heads directly to B. Position B is \(90 \mathrm{~km}\) from \(\mathrm{O}\) on a bearing of \(190^{\circ}\). (a) Calculate the distance \(\mathrm{AB}\). (b) Calculate the bearing the ship must follow from \(\mathrm{A}\) to arrive directly at \(\mathrm{B}\).