Edexcel A-Level Mathematics AS P1.3.1 Sine Rule Cosine Rule and Triangle Area Questions

Practise Edexcel IAL Mathematics P1.3.1 by choosing sine or cosine rules, applying one-half ab sin C and resolving ambiguous triangle angles.

Exam points

choose sine rule, cosine rule or 1/2ab sin C from the triangle information given
use s=rθ and A=1/2r^2θ to find arc lengths, sectors, perimeters and areas

[Maximum number: 5]

The sides of a triangle are in the ratio 2: 4: 5

(a)

Find the size of the largest angle of the triangle, in degrees, to one decimal place.

Given that the area of the triangle is $140 \mathrm{~cm}^{2}$

[ 2 ]

$5^2=2^2+4^2-2(2)(4)\cos\theta$ $\theta=108.2^\circ$

(b)

find the length of the shortest side, in cm , to one decimal place.

[ 3 ]

$140=\frac12(2x)(4x)\sin108.2^\circ$ $x^2=\frac{280}{8\sin108.2^\circ}=36.8\ldots$
Shortest side $=2\sqrt{36.8\ldots}=12.1\text{ cm}$
B1ft, M1, A1

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