Trigonometric ratios

The diagram shows triangle PQR

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

ABCD is a trapezium with one line of symmetry.

angle ADC = 60° AD = 12 cm DC = 47 cm

Work out the area of the trapezium. Give your answer correct to 3 significant figures. Show your working clearly.

ABCD is a trapezium with one line of symmetry.

angle ADC = 60° AD = 12 cm DC = 47 cm

Work out the area of the trapezium. Give your answer correct to 3 significant figures. Show your working clearly.

The diagram shows triangle PQR

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

The diagram shows a square-based pyramid ABCDE

EA = EB = EC = ED

M is the centre of the horizontal square base ABCD Q is the midpoint of AB Angle EQM 80

EA: AB n:1

Find the value of n Give your answer correct to 3 significant figures.

The diagram shows a cuboid ABCDEFGH with horizontal base ADEH

M is the midpoint of the base ADEH and P is the midpoint of the edge CF

Work out the size of angle BMP Give your answer correct to one decimal place.

The diagram shows right-angled triangle ABD

AB = 14 cm AD = 8 cm

C is the point on BD such that angle BAC = 38°

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

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.

The diagram shows a triangle ABC inside a semicircle.

A, B and C are points on the semicircle.

AB is the diameter of the semicircle.

Angle ACB = 90° Angle BAC = 50° AC = 18 cm

Work out the perimeter of the semicircle. Give your answer correct to 2 significant figures.

R and T are points on a circle, centre O

RT = 12 cm M is the midpoint of RT Angle ROM = 52

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

Here is a shape formed from two triangles ABC and CDE ACD and BCE are straight lines.

AC = 24 cm BC = 31 cm CE = 19 cm CD = 16 cm

Angle BAC = 64°

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

The diagram shows a triangular prism, ABCDEF, with a rectangular base ABCD

AB = 6 cm DE = 2.2 cm angle DAE = 18 angle ADE = 90

Work out the angle that BE makes with the plane ABCD Give your answer correct to one decimal place.

The diagram shows a solid prism ABCDEFGHIJ

The prism is such that each cross section is a pentagon where

AE = BC = x cm AB = 2 x cm ED = CD = 8 cm

angle EAB = angle CBA = 90° angle AED = angle BCD = 120°

Given that AG = BH = EF = DJ = CI = 12 cm

calculate the angle that AJ makes with the base ABHG of the prism. Give your answer correct to 3 significant figures.

The diagram shows triangle ABC

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

The diagram shows triangle ABC

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

The diagram shows the prism ABCDEFGHJK with horizontal base AEFG

^_`ab$ is a cross section of the prism where ABDE is a square BCD is an equilateral triangle

EF = 2AE M is the midpoint of GF so that JM is vertical.

Angle MAJ = y

The diagram shows two vertical phone masts, AB and CD, on horizontal ground.

AB = 6.2 m AC = 244 m CD = 30.7 m

Work out the size of the angle of depression of B from D Give your answer correct to one decimal place.

A zip wire is shown as the dashed line AC in the diagram.

The zip wire is supported by two vertical posts AB and CD standing on horizontal ground.

CD = 2.6 m BD = 12 m

The zip wire makes an angle x with the horizontal, as shown in the diagram. The design of the zip wire requires the angle x to be at least 5°

Work out the least possible height of the post AB Give your answer correct to 3 significant figures.

ABCD is a horizontal rectangular field.

A vertical pole, AE, is placed at the corner A of the field.

AE = 12 m AB = 18 m AD = 8 m

Calculate the size of the angle between EC and the plane ABCD 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 a vertical cliff with a vertical radio mast on top of the cliff and a buoy in the sea.

The height of the cliff is 100 metres. The buoy is at the point B that is d metres from the base of the cliff. The angle of elevation from B to the top of the cliff is 20°

Calculate the value of d. Give your answer correct to 3 significant figures.

The point A at the top of the radio mast is vertically above the top of the cliff. The angle of elevation from B to A is 25°

Calculate the height of the radio mast. Give your answer correct to 3 significant figures.

The diagram shows two hot air balloons. A is a point on the base of one of the balloons and B is a point on the base of the other balloon.

The distance between A and B is 500 metres. The angle of depression of B from A is 23

Calculate the vertical height of A above B. Give your answer correct to one decimal place.

ABC is an isosceles triangle in a horizontal plane. The point T is vertically above B.

Angle ABC = 140 AB = BC = 8 cm TB = 10 cm M is the midpoint of AC.

Calculate the size of the angle between MT and the horizontal plane ABC. Give your answer correct to one decimal place.

The diagram shows a prism ABCDEFGH with a horizontal base.

The base of the prism, EFGH, is a square of side 12 cm. Trapezium ADEF is a cross section of the prism where AF and DE are vertical edges.

DE = CH = 10 cm AD = BC = 15 cm

Work out the size of the angle between CF and the base EFGH. Give your answer correct to one decimal place.

Work out the length of BE. Give your answer correct to one decimal place.

The diagram shows a right-angled triangle.

Calculate the value of x. Give your answer correct to one decimal place.

The diagram shows cuboid ABCDEFGH.

AB = 5 cm AH = 4 cm The size of the angle between CH and the plane ABCD is 35°

Calculate the volume of the cuboid. Give your answer correct to 3 significant figures.

Here is a right-angled triangle.

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

Here is a right-angled triangle.

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

The diagram shows two right-angled triangles, DEF and EFG.

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

The diagram shows a cuboid ABCDEFGH.

EH= 9 cm, HG= 5 cm and GB= 6 cm.

Work out the size of the angle between AH and the plane EFGH. 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 cuboid ABCDEFGH.

For this cuboid

the length of AB: the length of BC: the length of CF = 4: 2: 3

Calculate the size of the angle between AF and the plane ABCD. Give your answer correct to one decimal place.

The diagram shows a solid pyramid ABCDE with a horizontal base.

The base, BCDE, of the pyramid is a square of side 10 cm.

The vertex A of the pyramid is vertically above the centre O of the base so that AB = AC = AD = AE

The total surface area of the pyramid is 360 cm²

Work out the size of the angle between AC and the base BCDE. Give your answer correct to 3 significant figures.

The diagram shows a right-angled triangle.

Five of these triangles are put together to make a shape.

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

ABCD is a trapezium.

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

The diagram shows a triangular prism.

AF = 10 cm, AB = 24 cm and BC = 8 cm. Angle FAB = angle ADC = angle BCD = 90

Work out the size of the angle between the line BE and the plane ABCD. Give your answer correct to 1 decimal place.