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

Calculate .

= ........................................... cm

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

Calculate the value of .

The diagram shows a right-angled triangle.

Calculate the value of .

= ...................................................

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

= ................................................m 

The diagram shows a rectangular playground . m and m.

Calculate .

............................ m [3]

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

Calculate the value of .

= ................................................. 

Use trigonometry to calculate the value of.

= ..............................................

Use trigonometry to calculate the value of .

= ................................................... 

The diagram shows a right-angled triangle.

Calculate the value of .

.............................................. 

Calculate the size of angle .

Angle  = ............................

Write down the exact value of cos30°

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

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  and  are both right-angled triangles.

Calculate the value of .

................................ 

The diagram shows a field in the shape of a trapezium. and .
Angle  = angle  = .

i) Show that , correct to the nearest metre.

[3]

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

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

Sam has a rectangular pond, .

i) Calculate .

 = ...............................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 and travels to , then to and then back to .
is due south of and is due west of .
= 39km and = 21 km.

i) Calculate .

.............................km [3]

ii) Calculate angle .

Angle = ......................[2]

iii) Find the bearing offrom .

[1]

A vertical flagpole, , stands on horizontal ground and is held by two ropes,  and .
and angle .

Using trigonometry, calculate .

= ...............................m 

Calculate .

.......................... m 

Triangles  and  are both right-angled triangles.

Calculate the value of .

................................

Calculate the value of .

.................................

and  are points on the circumference of a circle, centre . Angle .

.[1]

i) Use trigonometry to calculate angle .

Angle  = ............................. [2]

ii) Show that = 48cm.

[2]

iii) Work out the area of triangle .

........................... cm² [2]

iv) Work out the total shaded area.

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

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

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