1. 1
   Triangle ABC has a right angle at B, with AB = 6 cm and BC = 8 cm.

   (a)

   What is the length of the hypotenuse AC?

   [1 mark]

   • A$14$ cm
   • B$10$ cm
   • C$48$ cm
   • D$2$ cm

   (b)

   What is the size of angle BAC, correct to 1 decimal place?

   [1 mark]

   • A$36.9°$
   • B$60.0°$
   • C$45.0°$
   • D$53.1°$

   (c)

   What is the value of $\sin(ACB)$, given AC = 10 cm (from part (a))?

   [1 mark]

   • A$0.6$
   • B$0.8$
   • C$1.33$
   • D$0.75$

   Total for question 1: 3 marks

2. 2
   A tower stands on level ground. From a point 40 m from the base of the tower, the angle of elevation to the top of the tower is 35 degrees.

   (a)

   Find the height of the tower, correct to 3 significant figures.

   [2 marks]

   (b)

   If the angle of elevation had instead been measured as 40 degrees from the same distance of 40 m, would the calculated height of the tower be greater or smaller than your answer to part (a)? Give a reason.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A hiker walks from point A on a bearing of 070 degrees for a distance of 12 km to point B.

   (a)

   Find the eastward displacement of B from A, correct to 3 significant figures.

   [3 marks]

   (b)

   Find the northward displacement of B from A, correct to 3 significant figures.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   From the top of a vertical cliff 45 m high, the angle of depression to a boat at sea is 25 degrees. The boat is due south of the point directly below the observer.

   (a)

   Find the horizontal distance from the base of the cliff to the boat, correct to 3 significant figures.

   [4 marks]

   (b)

   Find the direct (straight-line) distance from the observer at the top of the cliff to the boat, correct to 3 significant figures.

   [4 marks]

   (c)

   The boat then sails directly away from the base of the cliff, continuing along the same line, until the angle of depression from the top of the cliff reduces to 15 degrees. Find the additional distance the boat has travelled, correct to 3 significant figures.

   [5 marks]

   Total for question 4: 13 marks

End of questions