TS EAMCET · Maths · Properties of Triangles
In \(\triangle A B C\), if \(a, b, c\) are in arithmetic progression and \(\mathrm{A}=2 \mathrm{C}\), then \(\mathrm{b}: \mathrm{c}=\)
- A \(4: 5\)
- B \(2: 3\)
- C \(5: 4\)
- D \(5: 6\)
Answer & Solution
Correct Answer
(C) \(5: 4\)
Step-by-step Solution
Detailed explanation
\(a, b, c\) are in AP \(\Rightarrow \sin \mathrm{A}, \sin \mathrm{B}, \sin \mathrm{C}\) are in \(\mathrm{AP}\) \(\Rightarrow \quad 2 \sin \mathrm{B}=\sin \mathrm{A}+\sin \mathrm{C}\) \(\Rightarrow \quad 2 \sin B=\sin 2 C+\sin C \quad[\because A=2 C]\)…
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