IGCSEMathsEdexcelMaths AHigherExam QuestionsGeometry & TrigonometrySine, Cosine Rule & Area of Triangles

Sine, Cosine Rule & Area of Triangles (Edexcel IGCSE Maths A: Higher): Exam Questions

Exam code: 4MA1

4 hours48 questions
Medium
Hard
Very Hard
1a
Sme Calculator2 marks

A B C is a triangle.

q1-medium-4-11-sine-cosine-rule-and-area-of-triangge-edexcel-gcse-maths

Work out the area of triangle A B C.
Give your answer correct to 3 significant figures.

How did you do?

1b
Sme Calculator3 marks

Work out the length of the side A B.
Give your answer correct to 3 significant figures.

How did you do?

2
Sme Calculator3 marks
q2-medium-4-11-sine-cosine-rule-and-area-of-triangge-edexcel-gcse-maths

Calculate the length of P R. Give your answer correct to 3 significant figures.

How did you do?

3a
Sme Calculator2 marks

The diagram shows parallelogram E F G H.

q14-4ma1-1h-qp-jan20-paper1-igcse-maths

table row cell E F space end cell equals cell space 9.3 space cm space end cell row cell F G space end cell equals cell space 14.7 space cm space end cell row cell Angle space E F G space end cell equals cell space 106 degree end cell end table

Work out the area of the parallelogram.
Give your answer correct to 3 significant figures.

.......................cm squared 

How did you do?

3b
Sme Calculator3 marks

Work out the length of the diagonal E G of the parallelogram. Give your answer correct to 3 significant figures.

.....................cm 

How did you do?

4
Sme Calculator3 marks

The diagram shows triangle space P Q R.

q18-paper1h-june2019-edexcel-igcse-maths

Calculate the length of P R.
Give your answer correct to 3 significant figures.

.........................cm

How did you do?

5
Sme Calculator3 marks

A triangle has sides of length 8 cm, 10 cm and 14 cm.

Work out the size of the largest angle of the triangle.
Give your answer correct to 1 decimal place.

How did you do?

6
Sme Calculator1 mark

Here is a triangle.

q17-paper-1h-june-2018-aqa-gcse-maths

Circle the correct equation.

fraction numerator sin space space x over denominator 42 end fraction space equals space fraction numerator sin space 15 degree over denominator 104 end fraction

fraction numerator x over denominator sin space 42 degree end fraction space equals space fraction numerator 15 over denominator sin space 104 degree end fraction

fraction numerator sin space space x over denominator 34 end fraction space equals space fraction numerator sin space 15 degree over denominator 104 end fraction

fraction numerator x over denominator sin space 42 degree end fraction space equals space fraction numerator 15 over denominator sin space 34 degree end fraction

How did you do?

7
Sme Calculator1 mark

Here is a triangle.

q18b-paper-1h-nov-2021-aqa-gcse-maths

Leah tries to use the sine rule to work out the size of angle x.
Here are the first two lines of her working.

table row cell fraction numerator x over denominator sin space 31 end fraction end cell equals cell fraction numerator 54 over denominator sin space 72 end fraction end cell row blank blank blank row x equals cell fraction numerator 54 space sin space 31 over denominator sin space 72 end fraction end cell end table

What error has she made in this working?

How did you do?

8
Sme Calculator3 marks

Work out the size of angle x.

q20-paper2h-june2017-aqa-gcse-maths

...............................degrees 

How did you do?

9
Sme Calculator4 marks

A ship sails from P to Q and then from Q to R.

Q is 12 miles from P, on a bearing of 080°

R is 28 miles from Q, on a bearing of 155°

q23-paper-2h-nov-2021-aqa-gcse-maths

Work out the direct distance from P to R.

How did you do?

10
Sme Calculator4 marks

A B C and A C D are triangles.

q16-paper-2h-june-2019-aqa-gcse-maths

The area of space A C D spaceis 80.5 cm2

Work out the area of A B C.
Give your answer to 3 significant figures.

...............................cm2 

How did you do?

11a
Sme Calculator3 marks

Liz and Tia are walking towards a shop along different straight paths.

The diagram shows their positions at 2 pm

q21-paper-2h-june-2018-aqa-gcse-maths

Assume they walk at the same speed.

Who will arrive at the shop first?
You must show your working.

How did you do?

11b
Sme Calculator1 mark

In fact, Liz walks at a faster speed than Tia.

How does this affect the answer to part (a)?

How did you do?

12
Sme Calculator3 marks

Here is a triangle.

q22-paper3h-nov2017-aqa-gcse-maths

Work out the length P R.

.................cm

How did you do?

13
Sme Calculator3 marks

In the triangle, angle y is obtuse.

q20-paper3h-specimen2015-aqa-gcse-maths

Work out the size of angle y.

...................degrees

How did you do?

14a
Sme Calculator4 marks

The diagram shows a triangular field PQR which is used to grow organic carrots.

q18-paper5-nov2020-ocr-gcse-maths

PQ = 100 m, PR = 80 m and angle RPQ = 30°.

In recent years, an average of 2.5 kg of carrots has been harvested from each square metre of  the field.

Use this information to work out the total mass of carrots that might have been harvested from the field in 2019.

......................................................kg 

How did you do?

14b
Sme Calculator1 mark

Why might the answer to partspace left parenthesis bold a right parenthesis spacebe unreliable?

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15a
Sme Calculator4 marks

ABC and ACD are triangles.

q17-paper4-nov2017-ocr-gcse-maths

Show that AC = 13.0 cm, correct to 3 significant figures.

How did you do?

15b
Sme Calculator3 marks

Calculate BC.

..................... cm 

How did you do?

16
Sme Calculator3 marks

Calculate length DF in this triangle.

q15a-paper4-nov2019-ocr-gcse-maths

..................................................... cm 

How did you do?

17
Sme Calculator4 marks

Calculate angle ACB in this triangle.

q15b-paper4-nov2019-ocr-gcse-maths

How did you do?

18
Sme Calculator4 marks

T is a radar tower.
A and B are two aircraft.
At 3pm

  • aircraft A is 3250km from T on a bearing of 015°

  • aircraft B is 4960km from T on a bearing of 057°.

q17-paper6-june2019-ocr-gcse-maths

Calculate the distance that was between aircraft A and aircraft B at 3pm.

....................................................... km 

How did you do?

1
Sme Calculator5 marks
q1-hard-4-11-sine-cosine-rule-and-area-of-triangge-edexcel-gcse-maths

Work out the length of  A D.
Give your answer correct to 3 significant figures.

How did you do?

2
Sme Calculator5 marks
q2-hard-4-11-sine-cosine-rule-and-area-of-triangge-edexcel-gcse-maths

A B C spaceis a triangle.

A B space equals space 8.7 space cm. space Angle space A B C space equals space 49 degree. space Angle space A C B space equals space 64 degree.

Calculate the area of triangle A B C. Give your answer correct to 3 significant figures.

How did you do?

3
Sme Calculator5 marks

The diagram shows triangle L M N.

q3-hard-4-11-sine-cosine-rule-and-area-of-triangge-edexcel-gcse-maths

Calculate the length of L N.
Give your answer correct to 3 significant figures.

How did you do?

4
Sme Calculator5 marks
q4-hard-4-11-sine-cosine-rule-and-area-of-triangge-edexcel-gcse-maths

A B C spaceis a triangle.
D is a point on A C.
Angle space B A D space= 45°
Angle space A D B space= 80°
A B = 7.4cm
D C = 5.8 cm

Work out the length of B C.
Give your answer correct to 3 significant figures.

How did you do?

5
Sme Calculator5 marks

A B C spaceis a triangle.

q5-hard-4-11-sine-cosine-rule-and-area-of-triangge-edexcel-gcse-maths

A C space= 8.4m
Angle space A C B space= 40°

The area of the triangle = 100 m2.

Work out the length of A B.
Give your answer correct to 3 significant figures.
You must show all your working.

How did you do?

6a
Sme Calculator4 marks

In triangle R P Q,

R P = 8.7 cm
P Q = 5.2 cm
Angle space P R Q space= 32°

Assuming that angle space P Q R spaceis an acute angle, calculate the area of triangle R P Q.
Give your answer correct to 3 significant figures.

How did you do?

6b
Sme Calculator1 mark

If you did not know that angle space P Q R spaceis an acute angle, what effect would this have on your calculation of the area of triangle R P Q?

How did you do?

7
Sme Calculator3 marks

The diagram shows the triangle P Q R.

q7-hard-4-11-sine-cosine-rule-and-area-of-triangge-edexcel-gcse-maths

P Q space equals space x space cm P R space equals space 2 x space cm
Angle Q P R space equals space 30 degree 

The area of triangle P Q R space equals space A space cm squared

Show that   x space equals space square root of 2 A end root

How did you do?

8
Sme Calculator4 marks

A B C spaceis an isosceles triangle.

q8-hard-4-11-sine-cosine-rule-and-area-of-triangge-edexcel-gcse-maths

Work out the area of the triangle.
Give your answer correct to 3 significant figures.

How did you do?

9
Sme Calculator3 marks

Here is a triangle X Y Z.

q13-4ma1-1h-qp-nov21-paper1-igcse-maths

The length X Z and the angles Y X Z and space X Y Z spaceare each given correct to 2 significant figures.

Calculate the upper bound for the length Y Z.
Give your answer correct to one decimal place.
Show your working clearly.

....................................................... cm 

How did you do?

10
Sme Calculator6 marks

Here is a quadrilateral P Q R S.

q18-paper1hr-june2018-edexcel-igcse-maths

Angle S R Q is acute.

Work out the size of angle S Q R.
Give your answer correct to 1 decimal place.

How did you do?

11
Sme Calculator5 marks

A shape is made by joining triangle space A B C spaceto a semicircle with diameter A C.

q29-paper-3h-nov-2020-aqa-gcse-maths

Work out the total area of the shape.

How did you do?

12a
Sme Calculator3 marks

Here is a triangular sail.

q26-paper3h-nov2019-aqa-gcse-maths

Vicky needs to buy waterproofing liquid for the sail.

She will put 3 coats of liquid on each side of the sail.
A litre of liquid covers 8.5 square metres of sail.

How many 1-litre bottles of liquid does Vicky need?

How did you do?

12b
Sme Calculator5 marks

Another sail is joined to the first sail as shown.

q26b-paper3h-nov2019-aqa-gcse-maths

x is an acute angle.

Work out the size of angle x.

How did you do?

13
Sme Calculator6 marks

The diagram shows triangle ABC with D on AC and E on AB. DE is a straight line.

q14-paper4-june2017-ocr-gcse-maths

AD = 28 m, AE = 41 m, DE = 22 m and BC = 64 m.

Calculate the length CD.

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

How did you do?

14
Sme Calculator7 marks

The diagram shows some land in the shape of a quadrilateral, ABCD.

q20-paper5-june2017-ocr-gcse-maths

AB = 3km, AD = 5km, CD = 12km and angle BAC = 30°.

The land is sold for £10 million per square kilometre.

Calculate the total cost of the land.

£ .............................................. million 

How did you do?

15
Sme Calculator5 marks

A, B and C are three towns.

The bearing of B from A is 105°
The bearing of C from B is 230°

The distance of C from A is 180 km.
The distance of C from B is 95 km.

Calculate the distance of B from A.
Give your answer correct to 3 significant figures.

How did you do?

16
Sme Calculator5 marks

The diagram shows a triangle A B C and a flagpole B F

Triangle ABC with sides 9m, 11m, 16m, and right angle at B. Ray BF is perpendicular to AC and 10m long. Diagram not accurately drawn.

A comma space B and C are points on horizontal ground. B F is vertical.

A B equals 9 space straight m space space space space space B C equals 11 space straight m space space space space space A C equals 16 space straight m space space space space space B F equals 10 space straight m

D is the point on A C such that angle B D C equals 90 degree

Work out the size of the angle of elevation of the point F from the point D
Give your answer correct to one decimal place.

How did you do?

17
Sme Calculator5 marks

The diagram shows the positions of three villages, A, B and C

Triangle ABC with sides AB 3.6 km, BC 8.4 km; angles at A 54°, B 132°; north lines from A, B; note states "Diagram NOT accurately drawn".

The bearing of B from A is 054°
The bearing of C from B is 132°

Melur walks from A to B
She then walks from B to C and from C to A

Melur walks at an average speed of 6 km/h

Work out the total time Melur takes.
Give your answer in hours and minutes

How did you do?

1
Sme Calculator5 marks
q1-vhard-4-11-sine-cosine-rule-and-area-of-triangge-edexcel-gcse-maths

The area of triangle space A B C space is 6 square root of 2 spacem2.

Calculate the value of x.
Give your answer correct to 3 spacesignificant figures.

How did you do?

2
Sme Calculator5 marks

A B C spaceand space A D C spaceare triangles.

q2-vhard-4-11-sine-cosine-rule-and-area-of-triangge-edexcel-gcse-maths

The area of triangle space A D C spaceis 56 m2

Work out the length of A B.
Give your answer correct to 1 decimal place.

How did you do?

3
Sme Calculator5 marks

A B C D spaceis a parallelogram.

q3-vhard-4-11-sine-cosine-rule-and-area-of-triangge-edexcel-gcse-maths

A C = 9 cm
D C space = 11 cm
Angle D A C = 100°

Calculate the area of the parallelogram.
Give your answer correct to 3 significant figures.

How did you do?

4
Sme Calculator6 marks
q4-vhard-4-11-sine-cosine-rule-and-area-of-triangge-edexcel-gcse-maths

A B C spaceis an acute-angled triangle.
space B A space= 7cm
B C  = 8cm

The area of triangle space A B C space is 18 cm2.

Work out the size of angle B A C.
Give your answer correct to 3 significant figures.
You must show all your working.

How did you do?

5
Sme Calculator6 marks

A B C spaceis an acute angled triangle.

q6-vhard-4-11-sine-cosine-rule-and-area-of-triangge-edexcel-gcse-maths

The area of triangle space A B C spaceis 19 cm2.

Work out the size of angle A C B.
Give your answer correct to 3 significant figures.

How did you do?

6
Sme Calculator5 marks
q7-vhard-4-11-sine-cosine-rule-and-area-of-triangge-edexcel-gcse-maths

A B C spaceis a triangle.
D is a point on A B.

Work out the area of triangle B C D.
Give your answer correct to 3 significant figures.

How did you do?

7
Sme Calculator6 marks

The diagram shows trianglespace P Q R

q23-4ma1-2h-qp-jan22-paper2-igcse-maths

P Q equals 1.6 space cm

P R equals 4.2 space cm

Angle space P R Q equals 18 degree

Given that angle space P Q R spaceis obtuse, work out the area of triangle space P Q R.
Give your answer correct to 3 significant figures.

How did you do?

8
Sme Calculator4 marks

The diagram shows triangle A B C

q22-4ma1-1hr-qp-jan22-paper1-igcse-maths

c space equals space 11.5 space spacecorrect to one decimal place
x space equals space 80     correct to the nearest whole number
y space equals space 75 space space   correct to the nearest whole number

Calculate the upper bound for the value of b Show your working clearly.
Give your answer correct to 3 significant figures.

How did you do?

9
Sme Calculator6 marks
q18-4ma1-2h-qp-june21-paper2-igcse-maths

A B C D is a quadrilateral where A comma space B comma space C and D are points on a circle.

A B space equals space 8 space cm
B C space equals space 7.5 space cm
Angle A B C space equals space 98 degree
Angle A C D space equals space 35 degree

Work out the perimeter of quadrilateral A B C D.
Give your answer correct to one decimal place.

....................................................... cm 

How did you do?

10
Sme Calculator5 marks

Here is a triangle X Y Z.

q21-paper1hr-jan2019-edexcel-igcse-maths

The perimeter of the triangle is k space cm.

Given that x space equals space y space minus space 1
find the value of k.
Show your working clearly.

k space equals            

How did you do?

11
Sme Calculator6 marks

The diagram shows a regular octagon A B C D E F G H.

q22-paper1hr-nov2020-edexcel-igcse-maths

Each side of the octagon has length 10 cm.

Find the area of the shaded region A C D E H.
Give your answer correct to the nearest cm squared

............................................. cm squared 

How did you do?

12
Sme Calculator5 marks

The diagram shows a logo.

A B E and D C E are congruent triangles.
B C E is a sector of a circle, centre E.

q25-paper2h-june2017-aqa-gcse-maths

Show that the area of the logo is 510 cm2 to 2 significant figures.

How did you do?

13
Sme Calculator6 marks

The diagram shows two circles with centre Oand a regular pentagon A B C D E

Pentagon ABCDE inscribed in a circle with centre O. Note states "Diagram NOT accurately drawn" on the right side.

A comma space B comma space C comma space D and E are points on the larger circle. The pentagon has sides of length 8 cm.

The diagram is shaded such that

shaded area = unshaded area

Work out the radius of the smaller circle. Give your answer correct to 3 significant figures

How did you do?