Trigonometry (Cambridge International IGCSE Mathematics): Exam Questions

Calculate the value of $x$.

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

The diagram shows a right-angled triangle Calculate AB.

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

The diagram shows a right-angled triangle.

Calculate the value of $x$.

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

The diagram shows a right-angled triangle.

Use trigonometry to calculate the value of $x.$

$x=$ .............................. [2]

The diagram shows a right-angled triangle.

Calculate the value of $x$.

$x=$............................ [2]

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°.

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

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 $X$.

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

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

Using trigonometry, calculate $BD$.

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

Extract:

A vertical flagpole, [B D], stands on horizontal ground and is held by two ropes, [A D] and [C D]. [A D = 15 m, B C = 10.7 m] and angle [D A B = 38°].

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 $O$.

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

i) Use trigonometry to calculate angle $BAC$.

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

ii) Show that $BC$ = 48cm.

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

........................... cm² [2]

iv) Work out the total shaded area.

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

The points $B$, $C$, and $D$ lie on the circumference of the circle, centre $O$.

The line $AB$ is a tangent to the circle at $B$.

Find the value of $x$ and the value of $y$.

$BC$ is $4$cm.

Hence, find the radius of the circle.

Round your answer to 3 significant figures.

Calculate the area of the circle.

Round your answer to 3 significant figures.

Calculate the value of the length $YZ$.

Find the interior angle at $X$.

The diagram shows a circle, centre $O$, with diameter $PQ$. $R$ is a point on the circumference.

$PR=5.2\mathrm{cm}$, and $PR=\frac{1}{3}PQ$. Angle $PQR=x^{\circ}$.

Give a geometrical reason why angle $PRQ$ is 90°.

Extract:

The diagram shows a circle, centre O, with diameter PQ.

R is a point on the circumference.

PR = 5.2 cm, and PR = 1/3 PQ.

Angle PQR = x°.

Angle PRQ is 90°.

Find the value of $x$.

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