AP EAMCET · Maths · Properties of Triangles
In triangle ABC, if \(\mathrm{a}=13, \mathrm{~b}=8, \mathrm{c}=7\), then \(\cos (\mathrm{B}+\mathrm{C})=\)
- A \(\frac{11}{13}\)
- B \(\frac{23}{26}\)
- C \(\frac{3}{4}\)
- D \(\frac{1}{2}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\( \mathrm{B}+\mathrm{C} = \pi - \mathrm{A} \) \( \cos(\mathrm{B}+\mathrm{C}) = \cos(\pi - \mathrm{A}) = -\cos(\mathrm{A}) \) \( \cos(\mathrm{A}) = \frac{\mathrm{b}^2 + \mathrm{c}^2 - \mathrm{a}^2}{2\mathrm{bc}} = \frac{8^2 + 7^2 - 13^2}{2 \cdot 8 \cdot 7} \)…
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