The smallest angle of the Delta ABC,when a = | vedclass

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Question

(A) The smallest angle is opposite to the smallest side. Comparing the sides: $a = 7$,$b = 4\sqrt{3} \approx 6.928$,and $c = \sqrt{13} \approx 3.605$.

Vedclass · Accepted Answer

$30$

Vedclass · Answer

(A) The smallest angle is opposite to the smallest side. Comparing the sides: $a = 7$,$b = 4\sqrt{3} \approx 6.928$,and $c = \sqrt{13} \approx 3.605$.Since $c Using the Law of Cosines: $\cos C = \frac{a^2 + b^2 - c^2}{2ab}$.$\cos C = \frac{7^2 + (4\sqrt{3})^2 - (\sqrt{13})^2}{2 	imes 7 	imes 4\sqrt{3}}$.$\cos C = \frac{49 + 48 - 13}{56\sqrt{3}} = \frac{84}{56\sqrt{3}} = \frac{3}{2\sqrt{3}} = \frac{\sqrt{3}}{2}$.Since $\cos C = \frac{\sqrt{3}}{2}$,we have $C = 30^o$.

The smallest angle of the $\Delta ABC$,when $a = 7, b = 4\sqrt{3}$ and $c = \sqrt{13}$,is .....$^o$

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