Edexcel IGCSE Math A 4.8.HC sine and cosine rules

Practise non-right-triangle questions by choosing sine rule, cosine rule or area reasoning from the sides and angles given in the diagram.

Exam points

Use the cosine rule to find a missing side or angle in a non-right triangle.
Use the sine rule when a matching side-angle pair is available in the diagram.
Apply non-right-triangle trigonometry inside quadrilateral or perimeter problems.

[Maximum number: 3]

The diagram shows parallelogram EFGH.

Diagram NOT accurately drawn
$E F=9.3 \mathrm{~cm}$ $F G=14.7 \mathrm{~cm}$
Angle $E F G=106^{\circ}$

Work out the length of the diagonal EG of the parallelogram.

Give your answer correct to 3 significant figures.
cm

$GE^{2}=9.3^{2}+14.7^{2}-2(9.3)(14.7)\cos106^\circ$ $GE^{2}=377.9\ldots$

Final answer:
GE=19.4

Accept 19.4 to 19.5.

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