CAIE IGCSE Mathematics Extended E6.5.2 Use the Formula Area of Triangle 2 1 Ab Sin C Questions

Practise Extended CAIE IGCSE Mathematics by applying 1/2ab sin C to triangle areas, reversing the formula for an angle, and combining component areas in quadrilateral or field problems with correct units.

Exam points

Calculate a triangle’s area from two sides and their included angle using 1/2ab sin C.
Reverse 1/2ab sin C to find an acute or obtuse angle from a given area.
Combine sine-area calculations across triangles, quadrilaterals or field contexts and carry units through the result.
Rearrange the sine-area formula to obtain sin C, using inverse sine only when the angle is requested.
Use sin 30° = 1/2 to calculate a triangle’s area exactly in a non-calculator question.
Equate a triangle’s sine area to a fraction of a sector area, then solve for its equal sides.
Use a sine-area calculation and the known total field area to find a perpendicular height.
Calculate triangular land area, convert square metres to hectares and find the price per hectare.
Divide a triangular land area by the land needed per house to find the greatest whole number.

[Maximum number: 2]

Figure for Question CAIE IGCSE Mathematics Extended E6.5.2 Use the Formula Area of Triangle 2 1 Ab Sin C Questions question 1 — CAIE IGCSE Mathematics Extended

The diagram shows a triangle with an acute angle marked $x^{\circ}$ .
The area of the triangle is $2143 \mathrm{~cm}^{2}$ .
Work out the value of x.

40.7 or 40.73 to 40.74
M1 for $\frac12\times92.5\times71\sin x=2143$ oe

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CAIE IGCSE Mathematics Extended E6.5.2 Use the Formula Area of Triangle 2 1 Ab Sin C Questions question 1