(C) Let the sides of the triangle be $a = 3, b = 5,$ and $c = 7.$Since the largest side is $c = 7,$ the largest angle is $\angle C.$Using the Law of C

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(C) Let the sides of the triangle be $a = 3, b = 5,$ and $c = 7.$Since the largest side is $c = 7,$ the largest angle is $\angle C.$Using the Law of Cosines: $\cos C = \frac{a^2 + b^2 - c^2}{2ab}$Substituting the values: $\cos C = \frac{3^2 + 5^2 - 7^2}{2 \times 3 \times 5}$$\cos C = \frac{9 + 25 - 49}{30} = \frac{-15}{30} = -\frac{1}{2}$Since $\cos C = -\frac{1}{2},$ we have $\angle C = \arccos(-1/2) = \frac{2\pi}{3}.$

Class 11 Mathematics Trigonometrical Equations Relation between sides and angles, Solutions of triangles

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If the lengths of the sides of a triangle are $3, 5, 7,$ then the largest angle of the triangle is

IIT 1994 All IIT

A
$\pi / 2$
B
$5\pi / 6$
C
$2\pi / 3$
D
$3\pi / 4$

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Relation between sides and angles, Solutions of triangles

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