Question

directions: select the best response.
pine street, rector street, and taylor street intersect to form a triangular shaped park as shown.
what is the correct order of the street lengths from longest to shortest?
taylor, pine, rector
rector, pine, taylor
rector, taylor, pine
pine, taylor, rector

Explanation:

Step1: Find the third angle

The sum of angles in a triangle is \(180^{\circ}\). Let the third angle be \(x\). Then \(x = 180-(54 + 64)=180 - 118=62^{\circ}\).

Step2: Apply the side - angle relationship

In a triangle, the larger the angle, the longer the side opposite it. The angles are \(64^{\circ}\), \(62^{\circ}\), \(54^{\circ}\). The sides opposite these angles (let's say side opposite \(64^{\circ}\) is \(a\) (Taylor Street), side opposite \(62^{\circ}\) is \(b\) (Pine Street), side opposite \(54^{\circ}\) is \(c\) (Rector Street)). Since \(64>62 > 54\), the order of sides from longest to shortest is Taylor, Pine, Rector.

Answer:

Taylor, Pine, Rector