Trigonometry (AQA GCSE Further Maths)

        

Work out the length of .

.......................[3]

Use the sine rule to work out the size of obtuse angle .

.............................. degrees[3]

VABCD is a pyramid with a horizontal rectangular base ABCD.

V is directly above the centre of the base.

VA = VB = VC = VD = 10 cm

AB = 8 cm BC = 6 cm

M is the midpoint of BC.

Work out the size of angle VMD.

............................ degrees[5]

Here is a triangle.

Use the cosine rule to work out the value of .

[4]

ABC is a triangle.

The perpendicular from meets at .

Area of triangle
Work out the length, in cm, of .
Give your answer in the form where and are integers.

........................cm[5]

is a right-angled triangle.

is a point on .
Angle = 45°
is the midpoint of .
is a constant.

Work out the coordinates of .

[3]

ABCDEFGH is a cube with side length 32 cm

and are points on and respectively.

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

...................degrees[5]

is a trapezium.

is a straight line.

is a square of side cm

Show that

[1]

Show that

[1]

Work out the perimeter of the trapezium .

Give your answer in the form where and are integers.
You must show your working.

..........................cm[3]

Here is a triangle.

Use the cosine rule to work out the ratio   

[3]

is a right-angled triangle.

is an isosceles triangle.

All dimensions are in centimetres.

Show that   

[1]

Work out an expression, in cm², for the area of quadrilateral .

Give your answer in the form where is an integer.

..........................cm²[5]

 is a cuboid.

= 15 cm    = 12 cm     = 8 cm

Work out the size of the angle between the line and the plane .

[4]

In triangle ABC,

AB =  cm, angle ABC = 45° and angle ACB = 60°

Work out the value of .

Give your answer in the form , where  and are integers.

You must show your working.

................................ cm[5]

PQRSTU is a triangular prism.

PQRS is a rectangle and angle QRU = 90°

PQ = 10 cm      QR = 12 cm      UR = 7 cm

M is the midpoint of PQ.

Calculate the size of the angle between the line UM and the plane PQRS.

 ........................ degrees[4]

Calculate the size of the angle between the planes UMR and UQR.

........................... degrees[2]

is a square.
is a straight line.

is cm and angle

Show that the side of the square is 3 cm

[2]

Show that the perimeter of trapezium is 

[4]

In triangle ,

Show that triangle is isosceles.

[4]

A triangle has vertices

      and   

Work out the area of triangle
You may use the grid to help you.

[3]

............................square units

Angle is acute.

where is a constant greater than 1

Work out the expression for sin

Give your answer in the form   where and are integers.

You may use a diagram to help you.

[4]

Pyramid has a horizontal rectangular base.

is the centre of the base.
is vertically above .

           

Work out the angle between the planes and .

[4]

.............................degrees