Right-Angled Triangles - Pythagoras & Trigonometry (CIE IGCSE Maths: Extended)

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

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.

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

Here is a rectangle.

The 8-sided shape below is made from 4 of these rectangles and 4 congruent right-angled triangles.

Work out the perimeter of the 8-sided shape.
You must show all your working.

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.

Trianglehas perimeter 20 cm.

= 7 cm.
= 4 cm.

By calculation, deduce whether triangle is a right-angled triangle.

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

Calculate the shortest distance from point to .

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