Question

identify the side lengths from longest to shortest?* a 100° b c 55° ab, ac, bc bc, ab, ac ac, ab, bc bc, ac, ab

Explanation:

Step1: Find the measure of angle \( B \)

Use the triangle - angle sum theorem (\( A + B + C=180^{\circ} \)). Given \( A = 100^{\circ}\) and \( C = 55^{\circ}\), then \( B=180^{\circ}-(100^{\circ}+55^{\circ})=25^{\circ}\).

Step2: Apply the side - angle relationship in a triangle

In a triangle, the larger the angle, the longer the side opposite it.
Since \( A = 100^{\circ}\), \( C = 55^{\circ}\), \( B = 25^{\circ}\), and side opposite \( A\) is \( BC\), side opposite \( C\) is \( AB\), side opposite \( B\) is \( AC\).
So, \( BC>AB>AC\) (because \( 100^{\circ}>55^{\circ}>25^{\circ}\)).

Answer:

BC, AB, AC