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Igcse Question In The Sunday Times

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barnaclebill58 | 17:53 Sun 17th Jun 2018 | Quizzes & Puzzles
2 Answers
LMNP is a quadrilateral.
LMN=58 degrees
NPL=72 degrees
MN=13.7cm
NP=4.3cm
PL =15.6cm
Work out to 3 significant figures angle MLP.

Can't see it-presumably the trick is to construct some right angled triangles and use some trig but can't see it.
Thanks
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Too many steps for me to follow it through to the end, but I think the solution arises from:

1. Drawing a line between corners L and N.
2. Using the cosine rule (a^2 = b^2 + c^2 - 2 b c Cos[A]) to work out the length of this line.
3. Using the Sine rule (a/Sin[A] = b/ Sin[B]) to work out angles NLP and NLM.
4. Summing these two angles.

This avoids the problem of trying to find a right-angled triangle.

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Ah _ I'd forgotten about those rules .

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