Pythagoras & Trigonometry (Edexcel 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 $\sin 60°$

Given that $\cos 60°=0.5$,
work out the value of $x$.

Write down the exact value of cos30°

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

$PQR$ is a right-angled triangle.

Calculate the length of $PQ$.

Give your answer correct to 2 decimal places.

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 

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.

Ted wants to build a single storey extension on the back of his house. The diagram shows a sketch of his plan.

The outer wall is 4 metres from the house wall.

Both walls are parallel to each other and perpendicular to the floor.

The height of the outer wall is 2 metres.

The perpendicular distance from the floor of the house wall to the windowsill above is 3.85 metres.

The slope of the roof must have a minimum angle of elevation of $20°$ to allow for drainage.

The roof joins the outer wall to the house wall and must meet the house wall below the windowsill.

Show that the extension roof will fit on the back of the house with the current measurements.

$PQRS$ is a trapezium.

A square has the same area as this trapezium.

Calculate the perimeter of the square.

Give your answer to 3 significant figures.