CAIE IGCSE Mathematics Extended E6.5 Non Ri…ngles

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: 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

[Maximum number: 2]

Figure for Question 2 — CAIE IGCSE Mathematics Extended

The area of the triangle is $50\text{ cm}^2$ .
Calculate the value of $\sin x$ .
$\sin x=$

0.427 or 0.4273 to 0.4274

M1 for $\frac12\times13\times18\times\sin x=50$ .

[Maximum number: 5]

Figure for Question 3 — CAIE IGCSE Mathematics Extended

The diagram shows the straight roads between town A, town B and town C. $A C=60 \mathrm{~km}, C B=87 \mathrm{~km}$ and B is due east of A.
The bearing of C from A is $038^{\circ}$ .

Show that angle $A C B=95.1^{\circ}$ , correct to 1 decimal place.

Angle $CAB=52^\circ$ $180-52-\sin^{-1}\left(\frac{60\sin52^\circ}{87}\right)$
M2 for $\sin^{-1}(\frac{60\sin52^\circ}{87})$ oe, or M1 for sine-rule setup
$95.08...^\circ$

All question bank results loaded

CAIE IGCSE Mathematics Extended E6.5 Non Right Angled Triangles Topic Practice

Covered syllabus points

Question 1

Question (a)

Question (i)

Question (ii)

Question 2

Question 3