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: 2]

Figure for Question 1 — CAIE IGCSE Mathematics Extended

The diagram shows a triangle with an acute angle marked $x^{\circ}$ .
The area of the triangle is $2143 \mathrm{~cm}^{2}$ .
Work out the value of x.

40.7 or 40.73 to 40.74
M1 for $\frac12\times92.5\times71\sin x=2143$ oe

[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

[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 ]

$\cos ACB=\frac{15^2+8^2-20^2}{2\times15\times8}$
117.54 to 117.55
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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CAIE IGCSE Mathematics Extended E6.5 Non Right Angled Triangles Topic Practice

Covered syllabus points

Question 1

Question 2

Question (a)

Question (b)

Question 3

Question (a)

Question (b)