Edexcel IGCSE Math A 4.8.HE triangle area using sine

Practise sine-area questions by identifying the two sides enclosing the angle and applying one-half ab sin C before rounding.

Exam points

Use the formula 1/2 ab sin C to calculate the area of a triangle or parallelogram.
Rearrange the sine-area formula to find a missing side from a given area.
Choose the included angle between the two given sides before substituting.

[Maximum number: 3]

The diagram shows isosceles triangle EFG

Figure for Question 4.8.HE Area of a triangle using 1/2 ab sin C question 1 — Edexcel IGCSE Math A Higher

E F=G F
Angle $E F G=130^{\circ}$
The area of triangle EFG is $74 \mathrm{~cm}^{2}$
Work out the length of EF
Give your answer correct to 3 significant figures.
cm

Since EF=FG,
$\frac12\times EF\times FG\times\sin 130^\circ=74$ $EF^{2}=\frac{2\times74}{\sin 130^\circ}=193.2\ldots$ $EF=\sqrt{193.2\ldots}=13.9\ldots$

Final answer:
$13.9\text{ cm}$

A1 awrt 13.9.

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4.8.HE Area of a triangle using 1/2 ab sin C question 1