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If Two Sides of a Triangle Are Unequal, Then the Angle Opposite to the Greater Side Is Greater Than Angle Opposite to the Smaller Side

In ABC , ∠ A ...

Question

In $∆$ ABC, $∠$ A = 40 $°$ , $∠$ B = 80 $°$ find the shortest and the longest side of $∆$ ABC. Justify.

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Solution

$Given : ∠ A = 40 °, ∠ B = 80 ° In △ ABC, ∠ A + ∠ B + ∠ C = 180 ° (a ngle sum property) \Rightarrow 40 ° + 80 ° + ∠ C = 180 ° \Rightarrow ∠ C = 60 ° Since, the side opposite the largest angle is longest and that opposite the shortest angle is shortest, side opposite ∠ A, i . e . BC is shortest and side opposite ∠ B, i . e . AC is longest .$

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In ∆ABC, ∠A = 40°, ∠B = 80° find the shortest and the longest side of ∆ABC. Justify.

In $∆$ ABC, $∠$ A = 40 $°$ , $∠$ B = 80 $°$ find the shortest and the longest side of $∆$ ABC. Justify.