CAIE IGCSE Mathematics E6.5 Non-right-angled triangles Question Bank

Practise using sine rule, cosine rule and triangle area formulae to calculate missing sides, angles, areas and contextual measures.

Exam points

choose sine or cosine rule from the given triangle data to calculate a side or angle
apply 1/2ab sin C to triangle, quadrilateral or field-area calculations

Covered syllabus points

E6.5.1 Use the sine and cosine rules in calculations involving lengths and E6.5.2 Use the formula area of triangle = 2 1 ab sin C

[Maximum number: 6]

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.

(a)

Show that angle $ACB=117.5^\circ$ , correct to 1 decimal place.

[ 4 ]

$\cos ACB=\frac{15^2+8^2-20^2}{2\times15\times8}$
M2
117.54 to 117.55
A2
A1 for $-\frac{37}{80}$ , $-\frac{111}{240}$ , or -0.4625

(b)

Calculate the area of triangle ABC.

[ 2 ]

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

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Covered syllabus points

E6.5 Non-right-angled triangles question 1

Question (a)

Question (b)