91Ó°ÊÓ

A \(23 \mathrm{~N}\) force acts at \(71^{\circ}\) to the horizontal axis. Resolve the force into forces acting horizontally and vertically.

Express the following angles in degree/minute/ second format. (a) \(11.1731^{\circ}\) (b) \(14.0017^{\circ}\) (c) \(36.9213^{\circ}\)

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.

\(\triangle \mathrm{ABC}\) has a right angle at B. Given \(\mathrm{AB}=7 \mathrm{~cm}, \mathrm{BC}=12 \mathrm{~cm}\), calculate the length of \(\mathrm{AC}\).

From a point \(26.3 \mathrm{~m}\) from the foot of a tower the angle of elevation to the top of the tower is 29.27^{\circ} . \text { Calculate the height of the tower. }

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.

A \(40 \mathrm{~N}\) force acts at \(54^{\circ}\) to the horizontal. Resolve the force into horizontal and vertical forces.

\(\triangle \mathrm{PQR}\) has a right angle at \(\mathrm{P}\). If \(\mathrm{PR}=3.2 \mathrm{~m}\), \(\mathrm{QR}=4.9 \mathrm{~m}\), calculate the length of \(\mathrm{PQ}\).

A tower is \(36 \mathrm{~m}\) high. Calculate the angle of elevation to the top of the tower from a point \(50 \mathrm{~m}\) from the base of the tower.

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 A to arrive directly at \(\mathrm{B}\).