Pythagoras' theorem

Use trigonometry to work out the value of x. You must show your working.

Use trigonometry to work out the value of x. You must show your working.

Use Pythagoras’ theorem to show that the value of x is between 10 and 11

Here is a right-angled triangle.

Use Pythagoras’ theorem to show that x = 0.8

Use trigonometry to work out the value of x.

Here is a right-angled triangle.

Use Pythagoras’ theorem to show that x = 0.8

Two right-angled triangles are joined to make a larger triangle.

Work out the size of angle x.

Use trigonometry to work out the value of x.

A diagonal of a rectangle is 23.7 cm long. The diagonal makes an angle of 52 ° with a side of length x cm

Work out the value of x.

x =

Use Pythagoras’ theorem to work out the value of x. Give your answer as a decimal.

Use Pythagoras’ theorem to work out the value of x. Give your answer as a decimal.

Use Pythagoras’ theorem to work out the value of x.

Use Pythagoras’ theorem to work out the value of x.

VABCD is a pyramid with a horizontal square base. X is the centre of the base. V is vertically above X. BD = 18 cm Angle VBX = 72 °

Work out the length of VB.

Use trigonometry to work out the size of angle w.

w = °

Use trigonometry to work out the size of angle w.

PQ is a diameter of a circle. QR is a tangent to the circle. PQ = QR PR = 10 cm

Work out the radius of the circle. Give your answer as a decimal.

A circle, centre O, has circumference 20 π cm Q is a point on the circle.

Work out the value of a. You must show your working.

Work out the size of angle x.

Use trigonometry to work out the value of x.

Use trigonometry to work out the value of x.

In this right-angled triangle, a = 16 cm a: c = 4: 5 Work out the area of the triangle.

A boat sails 35 km North from A to B. From B the boat sails to C and then back to A.

Show that the distance the boat sails from C to A is 79 km to the nearest km You must show your working.

Work out the bearing of A from C.

Use trigonometry to work out the value of x.

x = cm

Here is a triangle.

Use Pythagoras’ theorem to work out the value of y. Give your answer as a decimal.

Trapezium DEFG is formed by joining triangle DEH

ABC is similar to DEH. Work out the area of DEFG.

Here is a triangle.

Give your answer as a fraction in its simplest form.

Here is a different triangle.

x = 3 y Work out the size of angle y.

y = °

Use trigonometry to work out the size of angle x.

x = °

Use trigonometry to work out the size of angle x.

x = °

Here is a right-angled triangle.

Use trigonometry to work out the value of x.

Here is a right-angled triangle.

Use trigonometry to work out the value of x.

Here is triangle ABC.

Assume that angle ACB = 90 ° Work out the length AB.

The actual length AB is greater than the answer to part (a). What does this mean about angle ACB ? Tick one box.

Here is a cube with edge length x cm One diagonal is shown.

Circle the length, in centimetres, of the diagonal.

The total length, in centimetres, of the edges of the cube is a multiple of 18 Circle the correct statement.

x is a x is not a x might be a whole number whole number whole number

A pyramid has a square base. Each of the four sloping edges has length 10 cm

The total length of all eight edges is 68 cm Work out the area of the square base.

cm 2

Use trigonometry to work out the size of angle x.

Use trigonometry to work out the size of angle x.

This shape is made from two right-angled triangles and a rectangle.

Work out the size of angle x.

Right-angled triangle ABC is the cross section of a prism. AB = 5 cm BC = 12 cm M is the midpoint of CF. AM = 16 cm

Work out the volume of the prism.

Use Pythagoras’ theorem to work out the value of x.

Use Pythagoras’ theorem to work out the value of x.

An isosceles triangle has base 16 cm and perpendicular height 15 cm

Some of these triangles are used to make a large triangle.

Work out the perimeter of the large triangle.

Use trigonometry to work out the value of x.

Here is a cuboid. DH = 8 cm DB = 13 cm

Work out the size of angle DBH.

Using your answer to part (a), work out the size of angle ECG.

P (– 1, 1) is a point on the circle, centre O, radius r.

Work out the value of r. Circle your answer.

Here is a triangular sail.

Vicky needs to buy waterproofing liquid for the sail. She will put 3 coats of liquid on each side of the sail. A litre of liquid covers 8.5 square metres of sail. How many 1-litre bottles of liquid does Vicky need?

Another sail is joined to the first sail as shown.

x is an acute angle. Work out the size of angle x.

Here are two right-angled triangles.

Circle the value of y.

11 7.5 9 4

The diagram shows rectangle ABDE and right-angled triangle ABC. AC = 17 cm BC = 8 cm

BC: CD = 1: 2 Work out the area of rectangle ABDE.

The diagram shows rectangle ABDE and right-angled triangle ABC. AC = 17 cm BC = 8 cm

BC: CD = 1: 2 Work out the area of rectangle ABDE.

Here is a right-angled triangle.

Use trigonometry to work out the size of angle x.

The length of a diagonal of a cuboid is 20 cm The diagonal makes an angle of 24° with the base.

Work out the volume of the cuboid.

Here is a right-angled triangle.

Show that x = 12

ABC and ACD are triangles.

Work out the size of angle x.

Use trigonometry to work out the size of angle x.

Use trigonometry to work out the size of angle x.

Liz and Tia are walking towards a shop along different straight paths. The diagram shows their positions at 2 pm

Assume they walk at the same speed. Who will arrive at the shop first? You must show your working.

In fact, Liz walks at a faster speed than Tia. How does this affect the answer to part (a)?

All dimensions are in centimetres.

Use Pythagoras’ theorem to work out the exact value of

ABCDEF is a triangular prism which represents part of a hill. ABCF is the horizontal rectangular base. D is vertically above C.

Work out the height CD.

Jamil walks in a straight line from A to D.

Work out the size of angle DAC. You must show your working.

Circle your answer.

19.5 25.5 331.5 380.25

Here is a triangle.

Work out the length PR.

VABCD is a square-based pyramid. The horizontal base ABCD has side length 10 cm and centre M. Angle VMA is 90° Angle VAM is 68°

× area of base × perpendicular height

Work out the volume of the pyramid.

Work out the value of x as a decimal.

Use trigonometry to work out the length x.

Use trigonometry to work out the length x.

Sami is trying to work out the exact value of y using Pythagoras’ theorem.

Here is her working. 2 2 2 (2 y) = 6 + 8

What error has she made in her working?

Kai works out that y = 5 Mel says, ‘‘ y cannot be 5 because the hypotenuse should be the longest side and the other sides are longer than 5 cm’’ Is Mel correct? Tick a box.

Give a reason for your answer.

Rectangle ABCD is the horizontal base of a triangular prism ABCDEF. AE = BE E is vertically above M, the midpoint of AB. AB = 16 cm AE = 17 cm BC = 30 cm

Show that EM = 15 cm

Work out the size of angle ECM.