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  • If a=2, b=3, c=5 in triangle ABC , then C=?       Option: 1 <img alt="\frac{\pi}{3}" src="https://learn.careers360.com/latex

If a=2, b=3, c=5 in triangle ABC , then C=?       

Option: 1

\frac{\pi}{3}


Option: 2

\frac{\pi}{4}


Option: 3

\frac{\pi}{6}


Option: 4

None of these


Answers (1)

best_answer

 

 

Cosine Rule -

Cosine Rule

 

The Law of Cosines states that the square of any side of a triangle is equal to the sum of the squares of the other two sides minus twice the product of the other two sides and the cosine of the included angle. For triangles, with angles A, B, and C, and opposite corresponding sides a, b, and c, respectively, the Law of Cosines is given as three equations. 

 

\cos A=\frac{b^{2}+c^{2}-a^{2}}{2 b c} \quad \cos B=\frac{a^{2}+c^{2}-b^{2}}{2 a c} \quad \cos C=\frac{a^{2}+b^{2}-c^{2}}{2 a b}

 

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\cos C=\frac{a^{2}+b^{2}-c^{2}}{2 a b}\\ cos C=\frac{2^{2}+3^{2}-5^{2}}{2 \times 2\times3}\\=-1\\ \angle C=\pi

Posted by

Devendra Khairwa

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