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In a △ABC, if AB = 636\sqrt{3} cm, BC = 6 cm and AC = 12 cm, then ∠B is

  1. 120°

  2. 90°

  3. 60°

  4. 45°

Pythagoras Theorem

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Answer

Here greatest length is 12 cm and other lengths are 6 cm, 636\sqrt{3} cm.

In a △ABC, if AB = 6√3 cm, BC = 6 cm and AC = 12 cm, then ∠B is? Pythagoras Theorem, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

Note that 122 = 144 and 62 + (63)2(6\sqrt{3})^2 = 36 + 108 = 144.

Thus, 122 = 62 + (63)2(6\sqrt{3})^2.

Hence, ABC is right triangle with hypotenuse = AC = 12 cm.

So, angle opposite to AC i.e. ∠B = 90°.

Hence, Option 2 is the correct option.

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