The sides of triangle are 7 cm- 4- 3cm- and - 13 cm- Then the smallest angle is 30o-

Clearly c=√( 13 ) is smallest side and hence c is the smallest angle ∴cos C = a ^ 2 + b ^ 2 c ^ 2 2ab =√( 3 ) #160; 2 ∴ C=30^o ...

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Standard IX

Mathematics

Side-Angle Inequality Theorems

The sides of ...

Question

The sides of triangle are $7$ cm, $4 \sqrt 3$ cm, and $\sqrt{13}$ cm. Then the smallest angle is $30^{o}$ .

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Solution

Clearly $c = \sqrt{13}$ is smallest side and hence $c$ is the smallest angle
$∴ cos C = \frac{a^{2} + b^{2} - c^{2}}{2 a b} = \frac{\sqrt{3}}{2} ∴ C = 30^{o}$

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The sides of triangle are 7 cm, 4√3cm, and √13cm. Then the smallest angle is 30o.

Clearly c=√13 is smallest side and hence c is the smallest angle∴cosC=a2+b2−c22ab=√32∴C=30o

The sides of triangle are $7$ cm, $4 \sqrt 3$ cm, and $\sqrt{13}$ cm. Then the smallest angle is $30^{o}$ .

Clearly $c = \sqrt{13}$ is smallest side and hence $c$ is the smallest angle
$∴ cos C = \frac{a^{2} + b^{2} - c^{2}}{2 a b} = \frac{\sqrt{3}}{2} ∴ C = 30^{o}$