Trigonometry (Cambridge (CIE) IGCSE International Maths: Core): Exam Questions

Show that the value of $x$ is 27.2, correct to 3 significant figures.

Calculate the value of $x$.

$x$= ................................................. 

Use trigonometry to calculate the value of$p$.

$p$ = ..............................................

Use trigonometry to calculate the value of $x$.

$x$ = ................................................... 

The diagram shows a right-angled triangle.

Calculate the value of $x$.

$x=$ .............................................. 

Calculate the size of angle $BAC$.

Angle $BAC$ = ............................

The diagram shows a circle, centre $O$, radius 11 cm.

$C,F,G$ and $H$ are points on the circumference of the circle.

The line $AD$ touches the circle at $C$ and is parallel to the line $EG$. $B$ is a point on $AD$ and angle $ABO$ = 140°.

i) Give a reason why angle $BCO$ is 90°.

[1]

ii) Show that$BC$ = 13.11 cm, correct to 2 decimal places.

[3]

iii) Calculate $BH$.

$BH$ = ......................... cm [3]

A speedboat starts at $X$ and travels to $Y$, then to $Z$ and then back to $X$.

$Z$ is due south of $X$ and $Y$ is due west of $Z$.

$XY$ = 39km and $XZ$ = 21 km.

i) Calculate $YZ$.

$YZ=$.............................km [3]

ii) Calculate angle $YXZ$.

Angle $YXZ$ = ......................[2]

iii) Find the bearing of$Y$from $X$.

[1]

A vertical flagpole, $BD$, stands on horizontal ground and is held by two ropes, $AD$ and $CD$.

$AD=15\mathrm{m},BC=10.7\mathrm{m}$ and angle $DAB=38°$.

Using trigonometry, calculate $BD$.

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

Calculate $CD$.

$CD=$.......................... m 

Triangles $ABC$ and $BCD$ are both right-angled triangles.

Calculate the value of $y$.

$y=$................................

Calculate the value of $x$.

$x=$ .................................

$A,B$ and $C$ are points on the circumference of a circle, centre $O$.

[1]

$AB=20\mathrm{cm}\mathrm{and}AC=52\mathrm{cm}.$

i) Use trigonometry to calculate angle $BAC$.

Angle $BAC$ = ............................. [2]

ii) Show that $BC$ = 48cm.

[2]

iii) Work out the area of triangle $ABC$.

........................... cm² [2]

iv) Work out the total shaded area.

............................... cm² [3]