Cosine rule

In triangle ABC, AB = 8 cm, AC = 11 cm and angle BAC = 62°.

Work out the length of BC. Give your answer correct to 3 significant figures.

In triangle PQR, PQ = 9.4 cm, PR = 13.7 cm and angle QPR = 118°.

Calculate the length of QR. Give your answer correct to 3 significant figures.

In triangle ABC, AB = 7 cm, BC = 9 cm and AC = 11 cm.

Find the size of the largest angle of the triangle. Give your answer correct to 1 decimal place.

In triangle ABC, AB = 3 cm, AC = 5 cm and BC = √19 cm.

Find the size of angle BAC.

Triangle ABC and triangle PQR are described below.

1. For each of these, say whether the sine rule or the cosine rule should be used first. You do not need to calculate anything.
   (i) In triangle ABC, AB = 6 cm, AC = 9 cm and angle BAC = 40°. Find BC.
   (ii) In triangle ABC, angle A = 35°, angle B = 80° and BC = 7 cm. Find AC.
   (iii) In triangle ABC, AB = 5 cm, BC = 7 cm and AC = 10 cm. Find angle ABC.
2. In triangle PQR, PQ = 14 cm, angle QPR = 48° and angle PQR = 71°. Calculate the length of QR. Give your answer correct to 3 significant figures.

In triangle ABC, AB = 8 cm, BC = 12 cm and AC = 15 cm.

1. Work out the size of angle ABC. Give your answer correct to 1 decimal place.
2. Work out the area of the triangle. Give your answer correct to 3 significant figures.

In triangle ABC, AB = 9 cm, AC = 12 cm and angle BAC = 48°.

Work out the size of angle ABC. Give your answer correct to 1 decimal place.

The diagram shows quadrilateral ABCD. The diagonal BD splits it into triangles ABD and BCD.

In triangle ABD, AB = 7 cm, AD = 10 cm and angle BAD = 65°.

In triangle BCD, angle DBC = 40° and angle BCD = 68°.

Work out the length of CD. Give your answer correct to 3 significant figures.

Two ships leave a port at the same time.

Ship A sails 24 km on a bearing of 062°.

Ship B sails 31 km on a bearing of 148°.

Work out the distance between the two ships. Give your answer correct to 3 significant figures.