Trigonometric ratios

All lengths shown are in centimetres.

Use Pythagoras’ theorem to show that 4w² – 8w – 21 = 0

Work out the size of angle x.

ABCDEF is a triangular prism. ABCD is a rectangle and angle BCF is 90 ° AB = 14 cm BC = 8 cm CF = 6 cm M is the midpoint of EF.

Work out the size of angle BMD.

A solid cone has base radius 7 cm, perpendicular height h cm and slant height l cm

Work out the size of the angle between the slant height and the base.

ABCDEFGH is a cuboid. ABCD is horizontal. MN is vertical. The acute angle between the planes MNB and HDCG is 36°

Work out the length CN.

ABC is a triangle with perpendicular height AD.

BD: DC = 2: 3

Work out the size of angle w.

VABCD is a pyramid. The square horizontal base, ABCD, has side length 15 cm V is directly above the centre, X, of the base. VA = 28 cm

Work out the size of the angle that VA makes with ABCD.

Here is a sketch of y = cos x for values of x from 0 ° to 360 ° α is an obtuse angle measured in degrees. cos α = – k where k is a positive constant.

Tick (✓) two boxes that show expressions for x where cos x = – k

Here is a right-angled triangle.

You are given that a 5

Use trigonometry to work out the range of values of x.

ABCDEFGH is a cuboid.

AB = 40 cm BC = 9 cm CG = 20 cm P is a point on HG such that HP: PG = 3: 7 AP = 25 cm

Work out the size of angle APC.

ABCDEFGH is a cube with side length 32 cm M and N are points on DH and CG respectively.

Work out the size of the angle that the line BM makes with the plane ABCD.