Pythagoras & Trigonometry (AQA GCSE Maths: Foundation): Exam Questions

Calculate $PQ$.

$PQ$ = ........................................... cm

The diagram shows a rectangle 14cm by $w$cm.
The diagonal is 23 cm.

Calculate the value of $w$.

$w=.................................................$

The diagram shows a right-angled triangle.

Calculate the value of $x$.

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

The diagram shows a right-angled triangle $ABC$.
Calculate the length of $AB$.

$AB$ = ................................................m 

The diagram shows a rectangular playground $ABCD$. $AB=23.4$m and $AC=35.1$m.

Calculate $BC$.

$BC=$ ............................ m [3]

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 $BAC$ = ............................

Write down the exact value of cos30°

Given that sin30° = 0.5,
work out the value of $x$.

Find the missing angle $x$.

Give your answer to 3 significant figures.

The length of one side of a rectangle is 12cm.
The length of the diagonal of the rectangle is 13cm.

Calculate the area of the rectangle.

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

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

Calculate the value of $y$.

$y=$................................ 

The diagram shows a field in the shape of a trapezium. $AB=150\mathrm{m},BC=90\mathrm{m}$ and $CD=120\mathrm{m}$.
Angle $ABC$ = angle $BCD$ = $90°$.

i) Show that $AD=95m$, correct to the nearest metre.

[3]

ii) A fence is built around the perimeter of the field.
It costs $\$48$ to build each 5-metre section of the fence.
Calculate the cost of building this fence.

$\$$ .................................... [3]

Sam has a rectangular pond, $ABCD$.

i) Calculate $BC$.

$BC$ = ...............................m [3]

ii) He puts a fence around the edge of the pond. Calculate the length of the fence.

................................m [1]

The diagram shows a right-angled triangle.

Calculate the perimeter.

............................................ 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 $O$. Angle $ABC=90°$.

.[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]

The diagram shows two vertical phone masts, $AB$ and $CD$, on horizontal ground.

$AB=6.2\mathrm{m}$      $AC=244\mathrm{m}$     $CD=30.7\mathrm{m}$

Work out the size of the angle of depression of $B$ from $D$
Give your answer correct to one decimal place.