Questions: Which is the shortest side of the triangle? AC AB BC not enough information

Which is the shortest side of the triangle? AC AB BC not enough information
Transcript text: Which is the shortest side of the triangle? $\overline{A C}$ $\overline{A B}$ $\overline{B C}$ not enough information
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Solution

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Which is the shortest side of the triangle?

Find the missing angle.

The sum of angles in a triangle is 180°. We are given two angles, 35° and 125°. Let the third angle be \(x\). \(35 + 125 + x = 180\) \(160 + x = 180\) \(x = 180 - 160\) \(x = 20\) So, the third angle is 20°.

Relate the side lengths to the angles.

The shortest side is opposite the smallest angle. The smallest angle is 20° which is at vertex A. The side opposite to A is BC. Therefore, BC is the shortest side.

\(\boxed{\overline{B C}}\)

\(\boxed{\overline{B C}}\)

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