1. 1
   A gardener is designing a triangular flower bed ABC. Angle A = 40 degrees, angle B = 65 degrees, and the side $a$ (opposite angle A) = 8 cm on the scale plan.

   (a)

   Find angle C.

   [1 mark]

   • A65 degrees
   • B70 degrees
   • C80 degrees
   • D75 degrees

   (b)

   Using the sine rule, find the length of side $b$ (opposite angle B), correct to 1 decimal place.

   [1 mark]

   • A10.3 cm
   • B12.3 cm
   • C11.3 cm
   • D9.3 cm

   (c)

   Using the sine rule, find the length of side $c$ (opposite angle C), correct to 1 decimal place.

   [1 mark]

   • A11.0 cm
   • B12.0 cm
   • C13.0 cm
   • D10.5 cm

   Total for question 1: 3 marks

2. 2
   Two hikers set off from a campsite C. Hiker P walks 6 km from C on one bearing and hiker Q walks 9 km from C on another bearing. The angle between their two paths at the campsite is 50 degrees.

   (a)

   Use the cosine rule to calculate the direct distance PQ between the two hikers, correct to 1 decimal place.

   [2 marks]

   (b)

   Using the sine rule and your answer to part (a), find angle CPQ (the angle at hiker P's position), correct to 1 decimal place.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A landscaper is quoting for turf on a triangular plot of land ABC, where AB = 15 m, AC = 11 m and angle A = 55 degrees.

   (a)

   Calculate the area of the plot, correct to 1 decimal place.

   [3 marks]

   (b)

   Use the cosine rule to calculate the length of BC, correct to 1 decimal place.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A surveying team is mapping a triangular plot of land PQR for a new sports field. They measure PQ = 20 m, QR = 14 m, and angle QPR = 35 degrees.

   (a)

   Show that there are two possible values for angle PRQ, and find both values, correct to 1 decimal place.

   [4 marks]

   (b)

   Given that angle PRQ is the obtuse value found in part (a), find angle PQR and hence use the sine rule to find the length PR, correct to 1 decimal place.

   [4 marks]

   (c)

   Using PQ = 20 m, PR = 8.3 m (from part (b)) and angle QPR = 35 degrees, calculate the area of triangle PQR, correct to 3 significant figures.

   [5 marks]

   Total for question 4: 13 marks

End of questions