Q. 134.6( 14 Votes )

# In Δ *ABC*, if ∠*A*=40° and ∠*B*=60° . Determine the longest and shortest sides of the triangle.

Answer :

Given that in Δ *ABC*

∠A = 40^{o} and ∠B = 60^{o}

We have to find shortest and longest side.

We know that,

Sum of angles of triangle = 180^{o}

∠A + ∠B + ∠C = 180^{o}

40^{o} + 60^{o} + ∠C = 180^{o}

100^{o} + ∠C = 180^{o}

∠C = 180^{o} – 100^{o}

= 80^{o}

Now,

40^{o} < 60^{o} < 80^{o}

∠A < ∠B < ∠C

∠C is greater angle and ∠A is smaller angle.

As, ∠A < ∠B < ∠C

BC < AC < AB (Therefore, side opposite to greater angle is larger and side opposite to smaller angle is smaller)

Therefore, AB is longest, and BC is smallest or shortest side.

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