EduNinja

[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

[Maximum number: 8]

Figure for Question 2 — CAIE IGCSE Mathematics Extended

NOT TO SCALE

The diagram shows a field, ABCD, on horizontal ground.
$B C=192 \mathrm{~m}, C D=287.9 \mathrm{~m}, B D=168 \mathrm{~m}$ and $A D=205.8 \mathrm{~m}$ .

(a)

Calculate angle CBD and show that it rounds to $106.0^{\circ}$ , correct to 1 decimal place.

[ 4 ]

106.01 to 106.02
M2 for $\cos\angle CBD=\frac{192^2+168^2-287.9^2}{2\times192\times168}$ oe, or M1 for the implicit form.
A1 for -0.276 to -0.275.

(b)

Calculate the area of triangle BCD.

[ 2 ]

15500 or 15501 to 15503...
M1 for $0.5\times192\times168\times\sin106^\circ$ oe.

(c)

Tomas buys the triangular part of the field, BCD. The cost is $ 35750 per hectare.

Calculate the amount he pays.
Give your answer correct to the nearest $ 100.
[1 hectare $=10000 \mathrm{~m}^{2}$ ]

[ 2 ]

55400
FT $3.575\times$ their (b)(i) oe rounded to nearest 100.
M1 for figs $3575\times$ figs their (b)(i), or figs 554, or figs 5541 to figs 5543.

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

Question 1

Question (a)

Question (b)

Question 2

Question (a)

Question (b)

Question (c)