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Question: The smallest angle of the \(\Delta ABC,\) when \(a = 7,b = 4\sqrt{3}\) and \(c = \sqrt{13},\) is...

The smallest angle of the ΔABC,\Delta ABC, when a=7,b=43a = 7,b = 4\sqrt{3} and c=13,c = \sqrt{13}, is

A

30o30^{o}

B

15o15^{o}

C

45o45^{o}

D

None of these

Answer

30o30^{o}

Explanation

Solution

Smallest angle is opposite to smaller side

∴\therefore cos⁡C=b2+a2−c22ab=49+48−132×7×43=323=32\cos C = \frac{b^{2} + a^{2} - c^{2}}{2ab} = \frac{49 + 48 - 13}{2 \times 7 \times 4\sqrt{3}} = \frac{3}{2\sqrt{3}} = \frac{\sqrt{3}}{2}

⇒ ∠C=30o\angle C = 30^{o}