In △ ABC, ∠A = 60⁰, ∠B = 75⁰ and AB =\( 2 \sqrt 6\) cm. Find the length of side BC.
Answer
Correct Answer : c ) 6 cm
Explanation :According to the question
In △ ABC, ∠A = 60⁰ , ∠B = 75⁰ and AB = \( 2 \sqrt 6\) cm
In △ ABC (using angle sum property of the triangle)
∠A + ∠B + ∠C = 180⁰
60⁰ + 75 + ∠C = 180⁰
⇒ ∠C = 45⁰
We know that, Using Lami’s theorem
\({sin \ A \over a}={sin \ B \over b}={sin \ C \over c}\)
Substitute the values
\({sin \ 60⁰ \over BC}={sin \ 45⁰ \over 2 \sqrt 6}\)
⇒\(BC={2 \sqrt 6*{sin \ 60⁰ \over sin\ 45⁰}}\)
⇒\(BC=2 \sqrt6*{{\sqrt3 \over 2}\over {1 \over \sqrt2}}\)
⇒\(BC={{2 \sqrt6* \sqrt3* \sqrt2 } \over 2}\)
⇒ BC = 6 cm
Hence, (c) is the correct answer.
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