Question

if m∠tuw = m∠vuw = 62° and vw = 42, what is tw?

Explanation:

Step1: Identify congruent triangles

In right - triangles $\triangle TUW$ and $\triangle VUW$, $\angle TUW=\angle VUW = 62^{\circ}$, $\angle T=\angle V = 90^{\circ}$, and $UW$ is common. By the Angle - Angle - Side (AAS) congruence criterion, $\triangle TUW\cong\triangle VUW$.

Step2: Use congruent - triangle property

Since $\triangle TUW\cong\triangle VUW$, corresponding sides are equal. So, $TW = VW$.

Answer:

$42$