goodie127
Answered

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devishri1977

Answer:

Step-by-step explanation:

Sum of all angles of a triangle = 180

∠M + ∠N + ∠P = 180

∠M + 119 + 31 = 180

∠M + 150        = 180

             ∠M = 180 - 150

∠M = 30°

Use Sine Rule:

[tex]\dfrac{a}{Sin \ A}=\dfrac{b}{Sin \ B}\\\\\\\dfrac{10}{Sin \ 30}=\dfrac{n}{Sin \ 119}\\\\\\\dfrac{10}{\dfrac{1}{2}}=\dfrac{n}{ 0.8746}\\\\\\10*2= \dfrac{n}{0.87}\\\\20*0.87=n\\\\[/tex]

n = 17.4

[tex]\dfrac{p}{Sin \ P}=\dfrac{m}{Sin \ M}\\\\\\\dfrac{p}{Sin \ 31}=\dfrac{10}{Sin \ 30}\\\\\\\dfrac{p}{0.5150}=\dfrac{10}{\dfrac{1}{2}}\\\\\dfrac{p}{0.52}=10*2\\\\\dfrac{p}{0.52}=20\\\\\\p=20*0.52\\\\p =10.4[/tex]

p = 10.4

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