CAIE IGCSE Mathematics Extended E6.5.1 Use the Sine and Cosine Rules in Calculations Involving Lengths and Questions

Practise Extended CAIE IGCSE Mathematics by choosing the sine or cosine rule, calculating missing sides and angles, and resolving obtuse or ambiguous triangle cases with mark-scheme methods.

Exam points

Choose and apply the sine rule to find a missing side or angle when an opposite side–angle pair is known.
Apply the cosine rule for three known sides or for two sides with their included angle.
Resolve obtuse or ambiguous triangle angles and use the resulting value in a further sine- or cosine-rule calculation.

[Maximum number: 7]

NOT TO SCALE

The diagram shows three points A, B and C on horizontal ground. The bearing of C from A is $145^{\circ}$ and angle $A C B=38^{\circ}$ . $A C=65 \mathrm{~m}$ and $B C=95 \mathrm{~m}$ .

(a)

Show that $A B=59.3 \mathrm{~m}$ , correct to 1 decimal place.

[ 3 ]

$\sqrt{65^2+95^2-2\times65\times95\cos38}$
M1 for $65^2+95^2-2\times65\times95\cos38$
A1 for 3518.0 to 3518.1
59.31...

(b)

Angle BAC is obtuse.

Work out the bearing of B from A.

[ 4 ]

244.4 to 244.6
B3 for $\angle BAC=99.5$ or 99.6 or 99.49 to 99.58... isw or answer 225.4 to 225.5...
OR M2 for $\sin A=\frac{95\sin38}{59.3}$ oe or $\cos A=\frac{59.3^2+65^2-95^2}{2\times59.3\times65}$
or M1 for sine/cosine rule setup
M1dep for 145 + their BAC leading to answer

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CAIE IGCSE Mathematics Extended E6.5.1 Use the Sine and Cosine Rules in Calculations Involving Lengths and Questions question 1

Question (a)

Question (b)