What is $∠ B$ equal to?

Question

Question

Consider the following for the three (03) items that follow: The sides of a triangle ABC are AB=3cm, BC=5cm and CA=7cm.

This question was previously asked in

NDA-I (Mathematics) Official Paper (Held On: 13 Apr, 2025)

Answer 1

Calculation:

Given,

The sides of the triangle are: a = 5 Cm, b = 7 cm, c = 3 cm.

Apply the Cosine Rule to find angle B:

Using the Cosine Rule:

$ \cos B = \frac{a^2 + c^2 - b^2}{2ac} $

Substitute the values of a, b and c

$ \cos B = \frac{5^2 + 3^2 - 7^2}{2 \times 5 \times 3} = \frac{25 + 9 - 49}{30} = \frac{-15}{30} = -\frac{1}{2} $

Now, calculate angle B :

$ B = \cos^{-1}\left(-\frac{1}{2}\right) = 120^\circ $

Thus, angle B is $120^\circ $

Hence, the correct answer is Option 3.

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