Question

Triangle PQR has the following angle measures:• mZP = 59°• mZQ = 46°List the sides of the triangle in order from longestto shortest.= PR= QR= PQ

Answer 1

Note that the sum of the angles in a triangle is 180 degrees

Since we already have the measurement of two angles :

59 and 46

The third angle will be :

`180-59-46=75`

So we have :

`\begin{gathered} \angle P=59 \\ \angle Q=46 \\ \angle R=75 \end{gathered}`

Note that the sides opposite to the angles are :

`\begin{gathered} \angle P\rightarrow\overline{QR} \\ \angle Q\rightarrow\overline{PR} \\ \angle R\rightarrow\overline{PQ} \end{gathered}`

Also note that, the measurement of the sides are proportional to their corresponding angles.

Since :

`\angle Q<\angle P<\angle R`

The sides are :

`\overline{PR}<\overline{QR}<\overline{PQ}`

Therefore the correct order from longest to shortest is :

PQ - QR - PR