In - ABC- if - A -45- and - B -65- then the longest side of the triangle isA- ABB- CAC- None of the aboveD- BC

The correct option is D BCAs we know that the three angles of a triangle add up to 180^∘, Also, the other two angles are given as, ∠A = nbsp;45^∘ and ∠B nb ...

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Standard IX

Mathematics

Triangle Inequality 2

In Δ ABC, if ...

Question

In $Δ A B C$ , if ∠A = 45° and ∠B = 65°, then the longest side of the triangle is _______.

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None of the above

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Solution

The correct option is B BC
As we know that the three angles of a triangle add up to $180^{\circ}$ ,
Also, the other two angles are given as,
$∠$ A = $45^{\circ}$ and $∠$ B = $65^{\circ}$
Therefore, $∠$ C = $180^{\circ}$ - $45^{\circ}$ - $65^{\circ}$ = $70^{\circ}$

Now,
$∠ C > ∠ B > ∠ A$
Hence, the side opposite to $∠$ A, i.e., BC is the smallest and the side opposite to $∠$ C, i.e., AB is the largest.

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In ΔABC, if ∠A = 45° and ∠B = 65°, then the longest side of the triangle is _______.

In $Δ A B C$ , if ∠A = 45° and ∠B = 65°, then the longest side of the triangle is _______.