Question

Plum Apple Street Street Apple Street, Pear Street, and Plum Street intersect to form a triangular-shaped park as shown. Given the angle measures, order the lengths of the sides from shortest to longest. 52 Pear Street 2 Pear, Plum, Apple Plum, Apple, Pear Apple, Plum, Pear Apple, Pear, Plum

Answer 1

Considering the triangle, you have to remember that the length of the sides is proportional to the measure of its opposite angle.

Considering the angle's measures, to determine the order of the sides of the triangles, first, you must know the measure of the three angles.

The inner sum of the triangles add up to 180º, so you can calculate the third angle as:

`\begin{gathered} \angle1+\angle2+\angle3=180º \\ \angle3=180º-(\angle1+\angle2) \\ \angle3=180º-(78+52) \\ \angle3=180º-130 \\ \angle3=50º \end{gathered}`

Order the angles from least to greatest

50º < 52º < 78º

The side opposite to the 50º angle is Apple street

The side opposite to the 52º angle is Plum street

The side opposite to the 78º angle is Pear street

So the order of the sides from shortest to longest is

Apple-Plum-Pear