Edexcel IGCSE Math A 4.8 trigonometry and Pythagoras

Use this trigonometry page to choose Pythagoras or a trigonometric method, then calculate missing lengths or angles in 2D and 3D diagrams.

Exam points

Use Pythagoras to find missing lengths in right-angled triangle problems.
Choose sine, cosine or tangent to find a length or angle in a right triangle.
Apply advanced trigonometry such as elevation, bearings, sine rule or cosine rule.

Covered syllabus points

4.8.A Pythagoras' theorem in two dimensions 4.8.B Trigonometry in right-angled triangles 4.8.C Two-dimensional trigonometry and bearings 4.8.HA Trigonometric ratios of obtuse angles 4.8.HB Angles of elevation and depression 4.8.HC Sine and cosine rules 4.8.HD Pythagoras’ theorem in three dimensions 4.8.HE Area of a triangle using 1/2 ab sin C 4.8.HF Trigonometrical methods to solve problems in three

[Maximum number: 3]

Two circles, $C_{1}$ and $C_{2}$ , are drawn on a centimetre grid, with a scale of 1 cm for 1 unit on each axis.

The centre of circle $C_{1}$ is at the point with coordinates (-1,3) and the radius of $C_{1}$ is 13 cm.

The centre of circle $C_{2}$ is at the point with coordinates (7,18) and the radius of $C_{2}$ is 6 cm.

Work out the distance between the centre of $C_{1}$ and the centre of $C_{2}$

$(18-3)^2+(7-(-1))^2=15^2+8^2=289$ $\sqrt{289}=17$
Final answer:
17

[Maximum number: 3]

A zip wire is shown as the dashed line AC in the diagram.

Diagram NOT accurately drawn

The zip wire is supported by two vertical posts AB and CD standing on horizontal ground.

C D=2.6 \mathrm{~m} \quad B D=12 \mathrm{~m}

The zip wire makes an angle x with the horizontal, as shown in the diagram. The design of the zip wire requires the angle x to be at least $5^{\circ}$

Work out the least possible height of the post AB
Give your answer correct to 3 significant figures.

Required vertical rise for $5^\circ$ :
$12\tan5^\circ=1.04986\ldots$
Minimum height:
$AB=2.6+1.04986\ldots=3.64986\ldots$
Final answer:
3.65
Accept answers that round to 3.65.

[Maximum number: 5]

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

Figure for Question 4.8 Trigonometry and Pythagoras’ theorem question 3 — Edexcel IGCSE Math A Higher

The bearing of B from A is $054^{\circ}$
The bearing of C from B is $132^{\circ}$
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 $6 \mathrm{~km} / \mathrm{h}$
Work out the total time Melur takes.
Give your answer in hours and minutes.
hours
minutes

Angle:
$\angle ABC=54^\circ+(180^\circ-132^\circ)=102^\circ$

Cosine rule:
$AC=\sqrt{3.6^{2}+8.4^{2}-2(3.6)(8.4)\cos102^\circ} = 9.802\ldots$

Total time:
$\frac{9.802\ldots+8.4+3.6}{6}=3.633\ldots\text{ h}$

Final answer:
$3\text{ hours }38\text{ minutes}$

Accept 3 hours and 37 to 38 minutes.

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Covered syllabus points

4.8 Trigonometry and Pythagoras’ theorem question 1

4.8 Trigonometry and Pythagoras’ theorem question 2

4.8 Trigonometry and Pythagoras’ theorem question 3