In triangle ABC - AB - m 2- n 2- BC -2 mn and AC - m 2- n 2- the value of angle ABC is-A 90- B 30-C 60-D 45-

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Standard X

Mathematics

Pythagoras Theorem

In triangle A...

Question

In triangle ABC, AB=m²-n², BC=2mn and AC=m²+n², the value of angle ABC is-

A)90°

B)30°

C)60°

D)45°

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Solution

AB²+BC²=(m²-n²)²+(2mn)²
=m⁴+n⁴-2m²n²+4m²n²
=m⁴+n⁴+2m²n²
=(m²+n²)²
=AC²

Therefore angle ABC=90°

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In triangle ABC, AB=m²-n², BC=2mn and AC=m²+n², the value of angle ABC is- A)90° B)30° C)60° D)45°

AB²+BC²=(m²-n²)²+(2mn)² =m⁴+n⁴-2m²n²+4m²n² =m⁴+n⁴+2m²n² =(m²+n²)² =AC² Therefore angle ABC=90°

In triangle ABC, AB=m²-n², BC=2mn and AC=m²+n², the value of angle ABC is-

A)90°

B)30°

C)60°

D)45°

AB²+BC²=(m²-n²)²+(2mn)²
=m⁴+n⁴-2m²n²+4m²n²
=m⁴+n⁴+2m²n²
=(m²+n²)²
=AC²

Therefore angle ABC=90°