In a ABC - - ABC -30- and - ACB -45- Which is the longest side in this triangle-A- BCB- CAC- ABD- All are same in length

The correct option is A BC Angles in ABC are; ∠BAC = 180^∘ (30^∘ + 45^∘) = 105^∘. So, ∠BAC gt; ∠ACB gt; ∠CBA As we know that the side opposite to the ...

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Standard IX

Mathematics

Scalene Triangle

In a ABC , ∠ ...

Question

In a $△$ ABC, $∠$ ABC = $30^{\circ}$ and $∠$ ACB = $45^{\circ}$ . Which is the longest side in this triangle?

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All are same in length

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Solution

The correct option is B
BC

Angles in $△$ ABC are;

$∠$ BAC = $180^{\circ} - (30^{\circ} + 45^{\circ}) = 105^{\circ}$ .

So, $∠$ BAC > $∠$ ACB > $∠$ CBA

As we know that the side opposite to the larger angle is longer than the side opposite to the smaller angle.

So, BC > AB > CA,

Therefore, the side opposite to the largest angle will be the longest side.

Hence, BC is the longest side.

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In a △ABC, ∠ABC = 30∘ and ∠ACB = 45∘. Which is the longest side in this triangle?

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