CAIE IGCSE Mathematics E6.5.2 Use the formula area of triangle = 2 1 ab sin C

Practise using 1/2ab sin C to find triangle areas, reverse the formula for angles, and connect area results to wider problems.

Exam points

calculate a triangle area from two sides and the included angle using 1/2ab sin C
reverse the area formula to find an acute or obtuse angle from a given area
combine triangle areas in quadrilaterals or field contexts, including unit conversions

[Maximum number: 2]

NOT TO SCALE

The diagram shows triangle ABC on horizontal ground.
$A C=15 \mathrm{~m}, B C=8 \mathrm{~m}$ and $A B=20 \mathrm{~m}$ .
BP and CQ are vertical poles of different heights.
$B P=3 \mathrm{~m}$ and $C Q=4 \mathrm{~m}$ .
AQ and PQ are straight wires.

Calculate the area of triangle ABC.

53.2 or 53.19 to 53.23
M1 for $0.5\times8\times15\times\sin117.5^\circ$ oe

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E6.5.2 Use the formula area of triangle = 2 1 ab sin C question 1