MHT CET · Maths · Properties of Triangles
If the lengths of the sides of triangle are \(3,5,7\), then the largest angle of the triangle is
- A \(\frac{\pi}{2}\)
- B \(\frac{5 \pi}{6}\)
- C \(\frac{2 \pi}{3}\)
- D \(\frac{3 \pi}{4}\)
Answer & Solution
Correct Answer
(C) \(\frac{2 \pi}{3}\)
Step-by-step Solution
Detailed explanation
Let \(\mathrm{a}=3, \mathrm{~b}=5, \mathrm{c}=7 \)
\( \cos \mathrm{C}=\frac{\mathrm{a}^2+\mathrm{b}^2-\mathrm{c}^2}{2 \mathrm{ab}}=\frac{9+25-49}{2 \times 3 \times 5}=\frac{-15}{30}=-\frac{1}{2} \)
\( \therefore \angle C=\frac{2 \pi}{3}\)
\( \cos \mathrm{C}=\frac{\mathrm{a}^2+\mathrm{b}^2-\mathrm{c}^2}{2 \mathrm{ab}}=\frac{9+25-49}{2 \times 3 \times 5}=\frac{-15}{30}=-\frac{1}{2} \)
\( \therefore \angle C=\frac{2 \pi}{3}\)
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