Specimen Paper SPEC/5/TZ0 P2 Q7

Adam sets out for a hike from hos camp at point \(\mathrm{A}\). He hikes at an average speed of \(4.2\) km/h for \(45\) minutes, on a bearing of \(035^{\circ}\) from the camp, until he stops for a break at point \(\mathrm{B}\).

1. Find the distance from point \(\mathrm{A}\) to point \(\mathrm{B}\).

   [2]

Adam leaves point \(\mathrm{B}\) on a bearing \(114^{\circ}\) and continues to hike for a distance of \(4.6\) km until he reaches point \(\mathrm{C}\).

2. 1. Show that \(\mathrm{A\hat{B}C}\) is \(101^{\circ}\).

   2. Find the distance from the camp to point \(\mathrm{C}\).

      [5]

3. Find \(\mathrm{B\hat{C}A}\).

   [3]

Adam's friend Jacob wants to hike directly from the camp to meet Adam at point \(\mathrm{C}\).

4. Find the bearing that Jacob must take to point \(\mathrm{C}\).

   [3]

Jacob hikes at an average speed of \(3.9\) km/h.

5. Find, to the nearest minute, the time it takes for Jacob to reach point \(\mathrm{C}\).

   [3]