Question

list the angle measures of $\triangle bcd$ in order from smallest to largest. assume that $t$ is a positive number.

Explanation:

Step1: Compare side lengths

Given \(t>0\), \(44t < 94t\). In \(\triangle BCD\), side \(DC=44t\), side \(BD=94t\), side \(BC\) is unknown, and \(\angle D=90^\circ\).

Step2: Relate sides to angles

In a triangle, the smallest angle is opposite the shortest side, and the largest angle is opposite the longest side.

• Shortest side \(DC=44t\), opposite \(\angle B\)
• Side \(BD=94t\), opposite \(\angle C\)
• \(\angle D=90^\circ\) is the largest angle (since it's a right angle, and the sum of the other two angles is \(90^\circ\))

Answer:

\(m\angle B < m\angle C < m\angle D\)