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

[Maximum number: 4]

The diagram shows a roof support.

Figure for Question 4.8 Trigonometry and Pythagoras’ theorem question 1 — Edexcel IGCSE Math A Foundation

The roof support is made from four lengths of wood, A B, A C, B C and MC

A C=B C=9 \mathrm{~m} \quad A B=12 \mathrm{~m}

angle $A M C=90^{\circ}$
Lewis is going to buy lengths of wood to make the roof support.
The wood costs 21.50 euros per metre.
Each length of wood he buys has to be a whole number of metres.
Work out the total cost of the wood Lewis needs to buy.
Show your working clearly.

Diagram NOT accurately drawn
euros

$CM^2+\left(\frac{12}{2}\right)^2=9^2$ $CM=\sqrt{9^2-6^2}=\sqrt{45}=3\sqrt5=6.708\ldots$

Total wood length:
$6.708\ldots+9+9+12=36.708\ldots$

Cost:
$36.708\ldots\times21.50=789.23\ldots$

Using a 7 m purchased length for CM:
$(7+9+9+12)\times21.50=795.50$

Final answer:
795.50

SC B3 for awrt 789 if using $6.708\ldots$ directly.

[Maximum number: 4]

28 A B C is a right-angled triangle.

Diagram NOT accurately drawn

$A C=21 \mathrm{~cm} \quad B C=15 \mathrm{~cm} \quad$ angle $A B C=90^{\circ}$
The point D lies on AB such that $D B=9 \mathrm{~cm}$
Work out the size of angle ACD
Give your answer correct to one decimal place.

$\angle ACB=\cos^{-1}\left(\frac{15}{21}\right)=44.4\ldots^\circ$ $\angle DCB=\tan^{-1}\left(\frac{9}{15}\right)=30.9\ldots^\circ$ $\angle ACD=44.4\ldots^\circ-30.9\ldots^\circ=13.5\ldots^\circ$

Final answer:
$13.5^\circ$

Accept $13.4^\circ$ to $13.6^\circ$ .

[Maximum number: 4]

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

Diagram NOT accurately drawn

B is 234 km due north of A.
C is 356 km due east of A.
Work out the bearing of B from C.
Give your answer correct to the nearest degree.

$\tan(\angle BCA)=\frac{234}{356}$ $\angle BCA=\tan^{-1}\left(\frac{234}{356}\right)=33.317\ldots^\circ$

Bearing:
$270+33.317\ldots=303.317\ldots$

Final answer:
$303^\circ$

Accept 303 to 303.4.

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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