Physics, asked by kalasyamnamala, 11 months ago

Ifa:b:c=2: √6 : (√3+1) then angle C =​

Answers

Answered by sprao53413
7

Answer:

Please see the attachment

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Answered by priyarksynergy
0

Given the ratio of sides of a triangle, Find angle A.

Explanation:

  • Let there be a triangle ABC having sides of lengths a, b, and c, and The angle opposite to each side are A, B, and C respectively.
  • The cosine rule gives us a formula for finding cosine of angles in a triangle using the side lengths of that triangle, cosA=\frac{b^2+c^2-a^2}{2bc} \\\\cosB=\frac{a^2+c^2-b^2}{2ac} \\\\cosC=\frac{b^2+a^2-c^2}{2ab}    
  • Here we have the ratio of sides of the triangle.
  • Hence, we get the corresponding sides as, a=2x\ \ \  \ \ b=x\sqrt{6}\ \ \  \ \ c=x(\sqrt{3} +1)
  • Now from the cosine rule we get angle A as, cosA=\frac{(x\sqrt{6})^2 +(x(\sqrt{3} +1))^2-(2x)^2}{2x^2(\sqrt{6} )(\sqrt{3} +1)} \\cosA=\frac{6 +3+1+2\sqrt{3} -4}{(6\sqrt{2} +2\sqrt{6} )} \\cosA=\frac{2(3+\sqrt 3)}{2\sqrt{2}(3+\sqrt{3} ) } \\cosA=\frac{1}{\sqrt 2} \\->A=cos^{-1}(\frac{1}{\sqrt 2} )\\->A=\frac{\pi}{4}    
  • Hence the angle A for the given triangle is 45°.

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