Sine & cosine rules

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

BAC is a sector of a circle, centre A

BCD is a sector of a circle, centre C

Angle BAC = 40° Angle BCD = 130° Area of shaded segment = 28 cm²

Find the length of the arc BD Give your answer correct to 3 significant figures.

Here is a triangle ABC

The area of the triangle is (x² + x – 3.75) cm²

Find the size of the largest angle in triangle ABC Give your answer correct to the nearest degree.

The diagram shows a triangle ABC and a flagpole BF

A, B and C are points on horizontal ground.

BF is vertical.

AB = 9 m BC = 11 m AC = 16 m BF = 10 m

D is the point on AC such that angle BDC = 90°

Work out the size of the angle of elevation of the point F from the point D Give your answer correct to one decimal place.

Here is a parallelogram PQRS, in which angle SPQ is acute.

PQ = 6.1 cm PS = 3.8 cm

The area of the parallelogram is 18 cm²

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

Here is triangle ABC

Work out the value of x Give your answer correct to 3 significant figures.

The diagram shows quadrilateral ABCD

The angle BCD is acute.

Given that the area of triangle BCD = 405 cm²

work out the size of angle ABD Give your answer correct to one decimal place.

The diagram shows triangle PQR

PQ = 1.6 cm PR = 4.2 cm Angle PRQ = 18°

Given that angle PQR is obtuse,

work out the area of triangle PQR Give your answer correct to 3 significant figures.

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

Ship B is due north of ship A.

The bearing of ship C from ship A is 120

Calculate the bearing of ship C from ship B. Give your answer correct to the nearest degree.

The diagram shows parallelogram EFGH.

EF = 9.3 cm FG = 14.7 cm Angle EFG = 106°

Work out the area of the parallelogram. Give your answer correct to 3 significant figures.

Work out the length of the diagonal EG of the parallelogram. Give your answer correct to 3 significant figures.

The diagram shows the prism ABCDEF with cross section triangle ABC.

Angle BEC = 40° and angle ACB is obtuse. AC = 6 cm and CE = 13 cm

The area of triangle ABC is 22 cm²

Calculate the length of AB. Give your answer correct to one decimal place.

The diagram shows triangle PQR.

Give your answer correct to 3 significant figures.

A boat sails from point X to point Y and then to point Z.

Y is on a bearing of 280° from X. Z is on a bearing of 220° from Y.

The distance from X to Y is 3.5 km. The distance from Y to Z is 6 km.

Work out the bearing of Z from X. Give your answer correct to 1 decimal place.

Calculate the length of AB. Show your working clearly. Give your answer correct to 3 significant figures.

Here is a quadrilateral PQRS.

Angle SRQ is acute.

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

A triangle has sides of length 8 cm, 10 cm and 14 cm.

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