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In triangle abc angle A is equals to 60 degree prove that BC square equals to a b square + ac square -aB.ac

Posted by Kavita Kumari 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

Given: In {tex}\triangle{/tex}ABC,

To prove: BC² = AB² + AC² - AB.AC
Construction: Draw CE {tex}\perp{/tex} AB
Proof: In {tex}\triangle{/tex}BEC
BC² = CE² + BE² ..(i)
In {tex}\triangle{/tex}ACE, AC² = CE²+ AE²
CE² = AC² - AE² ..(ii)
from (i) and (ii)
BC²= AC² - AE² + (AB - AE)² ({tex}\because{/tex} BE = AB - AE)
BC² = AC² + AB² - 2AB.AE - 2AB{tex}\frac{1}{2}{/tex}AC
Since side opposite to 30° angel is half hypoteneuse.
In {tex}\triangle{/tex}ACE, AE = {tex}\frac{1}{2}{/tex}AC
BC² = AB² + AC² - AB.AC

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