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

The diagram shows a circle, centre O.

AB is a chord of length 12 cm.

M is the mid-point of AB and OM = 4.5 cm.

Calculate the radius of the circle.

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

$ABC$is an isosceles triangle.

Work out the area of the triangle.

Give your answer correct to 3 significant figures.

Calculate the length of $PR$.

Give your answer correct to 3 significant figures.

$ABC$is a right-angled triangle.

Work out the size of angle $ABC$.

Give your answer correct to 1 decimal place.

The length of the side $AB$is reduced by 1 cm.

The length of the side $BC$is still 7 cm.

Angle $ACB$is still 90°

Will the value of cos$ABC$increase or decrease?

You must give a reason for your answer.

A solid metal cone has radius 1.65 cm and slant height 4.70 cm.

Find the angle the slant height makes with the base of the cone.

The diagram shows a trapezium $ABCD$.

$AB$ is parallel to $DC$.

$AB=55\mathrm{m}$, $BD=70\mathrm{m}$, angle $ABD=40°$ and angle $BCD=32°$.

Calculate the shortest distance from $A$ to $BD$.

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

The straight line $AC$ has equation $y=4x+5$.

Calculate the acute angle between $AC$ and the $x$-axis.

In this question, all measurements are in metres.

The diagram shows a right-angled triangle.

Given that $x=3.82$ to 3 significant figures, calculate the smallest angle of the triangle.

In the pentagon $ABCDE$, angle $ACB$ = angle $AED$ = 90°. Triangle $ACD$ is equilateral with side length 12 cm.

$DE$ = $BC$ = 6 cm.

Calculate angle $BAE$.

Angle $BAE$ = ...............................................

Calculate $AB$.

$AB$ = ......................................... cm

Calculate $AE$.

$AE$ = ......................................... cm

The cross-section of a prism is a right-angled isosceles triangle with its equal sides each being 7 cm.

The length of the prism is 18 cm.

Calculate the total surface area of the prism.

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

$C$ lies on a circle with diameter $AD$.

$B$ lies on $AC$ and $E$ lies on $AD$ such that $BE$ is parallel to $CD$.

$AB$ = 21 cm, $CD$ = 18 cm and $BE$ = 13.5 cm.

Work out the radius of the circle.

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

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

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

A square, with sides of length $x$ 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 $x$.

Give your answer correct to 3 significant figures.

Here is triangle $ABD.$

The point $C$ lies on $BD$.

$AD=13\mathrm{cm}BC=8\mathrm{cm}\mathrm{angle}ADB=90°\mathrm{angle}CAD=20°$

Calculate the size of angle $BAC$.

Give your answer correct to $1$ decimal place.

The diagram shows the positions of three points $A$, $B$ and $C$ in a field.

Calculate the shortest distance from point $B$ to $AC$.

............................................. 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 $BAC$ is $82.8°$ 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, $BC$ is a vertical wall standing on horizontal ground $AB$. $AC$ = 76.7 m.

$D$ is the point on $AB$ where $AD$ = 58 m.

The angle of elevation of $C$ from $A$ is 26°.

The angle of elevation of $C$ from $D$ is 72°.

Calculate $BD$.  

$BD$ = .......................................... m