MHT CET · Maths · Properties of Triangles
With usual notations, if the lengths of the sides of a triangle are \(7 \mathrm{~cm}, 4 \sqrt{3} \mathrm{~cm}\) and \(\sqrt{13} \mathrm{~cm}\), then the measures of the smallest angle is
- A \(\frac{\pi}{2}\)
- B \(\frac{\pi}{6}\)
- C \(\frac{\pi}{3}\)
- D \(\frac{\pi}{4}\)
Answer & Solution
Correct Answer
(B) \(\frac{\pi}{6}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { Let } a=7, b=4 \sqrt{3}, c=\sqrt{13} \\ \therefore \quad & \cos C=\frac{a^2+b^2-c^2}{2 a b}=\frac{49+48-13}{2 \times 7 \times 4 \sqrt{3}}=\frac{\sqrt{3}}{2} \\ \therefore \quad & \angle C=\frac{\pi}{6}\end{aligned}\)
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