Question

In triangle abc,angle a=55 degree ang angle b=80 degree. Name the shortest and longest side

Answer 1

Answer :

• AC is largest side.
• AB is Shortest side.

Solution :

Given :

• $\angle A \: = 55\degree$
• $\angle B \: = 80\degree$

To Find :

• Largest and shortest side.

Let's solve,

we know that,

$\sf \red{\bigstar}\boxed{\tt Sum \: of \: all \: the \: sides \: of \: triangle \: = \: 180\degree}$

So,

$\sf \angle A+\angle B+\angle C=180\degree\\ \\\implies \sf 55\degree+80\degree+\angle C=180\degree\\\\\implies\sf 135\degree+\angle C=180\degree\\\\\implies\sf\angle C=180\degree-135\degree\\\\\implies\sf\overline{\boxed{\sf \angle C=45\degree}}$

As we know,

• If a Angle is largest then side opposite to that angle will also be largest.

Hence,

Largest angle is <B. So, AC is largest side.

• If a Angle is Shortest then side opposite to that angle will also be Shortest.

Hence,

Shortest angle is <C. So, AB is Shortest side.

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