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: 5]

(a)

Figure for Question (a) — CAIE IGCSE Mathematics Extended

The area of triangle ABC is $62.89 \mathrm{~cm}^{2}$ .

[ 5 ]

(i)

Show that angle B A C=28.4^, correct to 1 decimal place.

[ 2 ]

$\frac12\times12.3\times21.5\times\sin(\ldots)=62.89$ or better
28.40 to 28.41...

(ii)

Calculate BC.
cm

[ 3 ]

12.2 or 12.17 to 12.18
M2 for $\sqrt{12.3^2+21.5^2-2\times12.3\times21.5\times\cos28.4}$
OR M1 for $12.3^2+21.5^2-2\times12.3\times21.5\times\cos28.4$
A1 for 148 or 148.2 to 148.3

All question bank results loaded

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

Question (a)

Question (i)

Question (ii)