Question

the sides of a tringle are 7cm,5cm,3cm. Then the largest angle of the tringle is​

Answer 1

➲Given that,the sides of a tringle are 7,5,3cm

To Find: the largest angle

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$\sf \underline\purple{ \bigstar \: analasyis \: of \: the \: queastion : }$

⇨ here as we have to find the largest angle we use cosines law.

Solution:

➧let the angle be x

★we know that, largest angle is opposite to the longest side.

$\sf {\underline {\underline {\orange{ \maltese \: as \: per \: cosies \: law : }}}}$

$\longmapsto \sf \: {7}^{2} = {5}^{2} + {3}^{2} - 2 \times 5 \times 3 \cos(x) \\ \\ \\ \longmapsto \sf \: 49 = 25 + 9 - 30 \cos(x) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longmapsto \sf \: 49 - 25 - 9 = - 30 \cos(x) \: \: \: \: \: \: \: \: \: \\ \\ \\ \longmapsto \sf \: 15 = - 30 \cos(x) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longmapsto \sf \: \cos(x) = - \frac { 15}{30} = - \frac{1}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longmapsto \sf \: x = 120 \degree \pink\bigstar \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\rm\underline \pink { \therefore \: the \: angle \: is \: 120 \degree}$