Question

Which should you use to find the length of a?

Answer 1

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➷ Pythagoras' theorem is only suitable for right triangles, which this isn't.

The Sine rule would not be applicable as there isn't any side and paired angle given

The best option for this would be the Law of Cosines as it is suitable for when you are given two sides and an angle between the.

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Answer 2

Answer:  Third option is correct.

Step-by-step explanation:

Since we have given that

ABC is triangle with its dimensions:

AB = 11

AC = 13

∠A = 108°

BC = a

We need to find the length of 'a'.

So, we can use "Law of cosines" as we have given two sides and one angle.

So, it becomes,

$\cos A=\dfrac{b^2+c^2-a^2}{2bc}\\\\\cos 108^\circ=\dfrac{11^2+13^2-a^2}{2\times 13\times 11}\\\\-0.3=\dfrac{121+169-a^2}{286}\\\\-0.3\times 286=290-a^2\\\\-85.8=290-a^2\\\\-85.8-290=-a^2\\\\375.8=a^2\\\\a=\sqrt{375.8}\\\\a=19.38$

Hence, Third option is correct.