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NDA 2017 Maths · Mathematics · Properties of Triangles · easy

The angle B is

Single correct option

In a triangle ABCABC, a=5a=5, b=7b=7 and c=8c=8. The angle BB is
  1. A. 30∘30^\circ
  2. B. 45∘45^\circ
  3. C. 90∘90^\circ
  4. D. 60∘60^\circ
Show answer and solution

Answer: (D) 60∘60^\circ

Cosine rule: cos⁡B=a2+c2−b22ac=25+64−4980=12\cos B=\dfrac{a^2+c^2-b^2}{2ac}=\dfrac{25+64-49}{80}=\dfrac12, so B=60∘B=60^\circ. The side opposite BB is b=7b=7, not cc; using the wrong side gives a different angle.
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Original question written in the NDA 2017 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake