Sine & cosine rules

The diagram shows triangle ABC.

AC = 12 cm, angle CAB = 40 ° and angle ABC = 58 °.

Calculate length BC.

The diagram shows a quadrilateral ABCD. DB is a diagonal of the quadrilateral.

AD = 5 cm, AB = 7 cm and BC = 14 cm. Angle DAB = x ° and angle DBC = 45°.

cos x ° = 0.8 and sin x ° = 0.6.

Work out the area of triangle BDC. You must show your working.

AC is a diagonal of the quadrilateral ABCD.

AD = 72 m. Angle ABC = 108 °, angle BCA = 3 8 ° and angle BAC = 34 °. Angle ACD = 90 °, angle CD A = 65 ° and angle CAD = 25 °.

Find the area of ABCD. You must show your working.

The diagram shows two triangles ABC and ADC.

Angle ABC = 60 °, angle ACB = 20 ° and angle ACD = 55 °. AB = 8 cm and DC = 6 cm.

Calculate length AD. You must show your working.

The diagram shows the positions of three towns A, B and C.

The bearing of town B from town A is 053°. The bearing of town C from town B is 108°. AB = 35 km and BC = 61 km.

Calculate AC. You must show your working.

A, B and C are points on the circumference of a circle.

Points C and D lie on a tangent to the circle at C. Angle BCD = 45 °. Angle ACB = 58°. AB = 8cm.

Find the length of BC.

The diagram shows triangle ABC.

AB = 10.6 cm, BC = 8.2 cm and AC = 12.5 cm.

Show that angle BAC = 40.5°, correct to 1 decimal place.

Work out the area of triangle ABC.

PQS and QRS are triangles.

PQ = 9 cm, QR = 8 cm and RS = 13 cm. Angle QPS = 30° and angle PSQ = 15°.

Calculate angle QSR. Give your answer correct to 1 decimal place. You must show your working.

The diagram shows triangle ABC. X lies on BC such that angle AXC = 90 °.

BC = 7.5 cm, angle ABC = 32 ° and angle ACB = 43 °.

Work out length AX. You must show your working.

The diagram shows triangle ABC.

AC = 48 mm, BC = 85 mm and angle BAC = 53°.

Calculate length AB. You must show your working.

The diagram shows triangle ABC.

AC = 15 cm, BC = 18 cm and angle BAC = 72°.

Calculate length AB, giving your answer correct to 3 significant figures. Show your working.

Calculate length DF in this triangle.

Calculate angle ACB in this triangle.

T is a radar tower. A and B are two aircraft.

At 3pm

• aircraft A is 3250 km from T on a bearing of 015°

• aircraft B is 4960 km from T on a bearing of 057°.

Aircraft A flies directly towards radar tower T at a speed of 890 km/h.

At what time will the aircraft pass over radar tower T? Give your answer to the nearest minute.

Calculate the distance that was between aircraft A and aircraft B at 3pm.

In this triangle:

• AB = 9 cm

• AC = 10 cm

• BC > 5 cm

• angle BCA = 60°

• angle ABC < 90°.

Calculate the area of triangle ABC.

Calculate the area of this triangle.

ABC and ACD are triangles.

Show that AC = 13.0 cm, correct to 3 significant figures.

Calculate BC.