Sine rule

In triangle ABC, angle BAC = 35°, angle ABC = 78° and BC = 9.4 cm.

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

In triangle ABC, angle BAC = 52°, angle ACB = 63° and AC = 11 cm.

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

In triangle ABC, AB = 12.5 cm, BC = 8.4 cm and angle BAC = 33°.

Angle ACB is acute.

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

In triangle PQR, QR = 14.2 cm, PR = 9.6 cm and angle QPR = 81°.

Calculate the size of angle PQR. Give your answer correct to 1 decimal place.

B is due east of A. AB = 250 m.

The bearing of a mast C from A is 040°.

The bearing of C from B is 300°.

Work out the distance AC. Give your answer correct to 3 significant figures.

In triangle ABC, angle ABC = 45°, angle ACB = 60° and AB = 6√2 cm.
Without using a calculator, show that AC = 4√3 cm.

In triangle ABC, angle BAC = 30°, BC = 5 cm and AB = 8 cm.

Work out the exact value of sin C.

In triangle ABC, AB = 10 cm, BC = 7 cm and angle BAC = 40°.
Angle ACB could be acute or obtuse. Work out both possible sizes of angle ACB. Give each answer correct to 1 decimal place.

A triangular sail has angles of 71° and 44°.

The side opposite the 71° angle has length 6.4 m.

Work out the length of the side opposite the 44° angle. Give your answer correct to 3 significant figures.

A boat leaves harbour H and sails 8 km on a bearing of 070° to a buoy B. A lighthouse L is due north of H. From B, the bearing of L is 320°.
Sketch the triangle HBL, then work out the distance HL. Give your answer correct to 3 significant figures.

In triangle ABC, angle BAC = 25°, BC = 7.2 cm and AB = 13.5 cm.

Angle ACB is obtuse.

Work out the size of angle ACB. 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, angle DAB = 58°, angle ABD = 47° and AD = 9.3 cm.

In triangle BCD, angle DBC = 39° and angle BCD = 64°.

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

In triangle ABC, angle BAC = 50°, angle ABC = 70° and AC = 12 cm.
Work out the area of triangle ABC. Give your answer correct to 3 significant figures.

In triangle ABC, AB = 12 cm, angle BAC = 40° and angle ABC = 75°.

Work out the perimeter of the triangle. Give your answer correct to 3 significant figures.

In triangle ABC, the point D lies on the side BC. The line AD bisects angle BAC.
Use the sine rule in triangles ABD and ACD to prove that BDDC = ABAC