Right-Angled Triangles: Pythagoras & Trigonometry (Cambridge O Level Maths)

ABDF is a parallelogram and BCDE  is a straight line.
AF = 12cm, AB = 9 cm, angle CFD = 40° and angle FDE = 80°.

Calculate the height, , of the parallelogram.

........................................... cm

The diagram shows a right-angled triangle.

............................................ cm

The diagram shows a right-angled triangle.

Calculate the value of .
 

= ............................................

The diagram shows a prism with length 18 cm and volume 253.8 cm³.
The cross-section of the prism is a right-angled triangle with base 6 cm and height  cm.

Calculate the value of .
 

= ...............................................

Calculate the total surface area of the prism.
 

........................................ cm²

The diagram shows a circle, centre O.
The straight line ABC is a tangent to the circle at B.
OB = 8 cm, AB = 15 cm and BC = 22.4 cm.
AO crosses the circle at X and OC crosses the circle at Y.
 
Calculate angle XOY.
 

Angle XOY = .............................................

In the diagram, AB and CD are parallel.
AD and BC intersect at right angles at the point X.
AB = 10 cm, CD = 5 cm, AX = 8 cm and BX = 6 cm.

Angle XAB = ..............................................

Calculate the length of AC.

AC = ........................................ cm

Calculate AC.

AC = .................................... m

Here is a right-angled triangle.

Work out the length of .
Give your answer correct to 1 decimal place.

Here is part of a field.

This part of the field is in the shape of a trapezium.
A farmer wants to put a fence all the way around the edge of this part of the field.

The farmer has 50m of fence.

Does he have enough fence?
You must show all your working.

The diagram shows a rectangular framework.

The framework is made from 5 metal rods.
The metal rods have a weight of 0.9 kg per metre.

Work out the total weight of the framework.
Give your answer, in kg, correct to 3 significant figures.

is a right-angled triangle.
= 9.6 cm.
= 6.4 cm.

Calculate the size of the angle marked .
Give your answer correct to 1 decimal place.

is a right-angled triangle.
 = 17 cm
= 25 cm

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

is a right-angled triangle.

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

is a right-angled triangle.

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

The diagram shows a rectangle and a diagonal of the rectangle.

Work out the length of the diagonal of the rectangle.
Give your answer correct to 1 decimal place.

.....................

The diagram shows the positions of three points , and in a field.

Calculate the shortest distance from point to .

............................................. m

The diagram shows a field ABCD.
The bearing of B from A is 140°. 
C is due east of B and D is due north of C.
AB = 400m, BC = 350m and CD = 450m.

Calculate the distance from D to A.
 

 ............................................. m

The angle  is correct to 3 significant figures.

D is the point on AC that is nearest to B.

Calculate the distance from D to A.

................................................ m

The diagram shows a field ABCDE.

Calculate the perimeter of the field ABCDE.
 

................................................ m

In the diagram, is a vertical wall standing on horizontal ground .
= 76.7 m.
is the point on where = 58 m.
The angle of elevation of from is 26°.
The angle of elevation of from is 72°.

Calculate .
 

= .......................................... m

Point A has co-ordinates (1, 0) and point B has co-ordinates (2, 5).

Calculate the angle between the line AB and the -axis.

A square, with sides of length  cm, is inside a circle.
Each vertex of the square is on the circumference of the circle.

The area of the circle is 49 cm².

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

Here is triangle 

The point  lies on .

Calculate the size of angle .
Give your answer correct to  decimal place.