Question

find the largest angle of △stu. assume that v is a positive number.

Explanation:

Step1: Identify given sides/angle

$\angle U = 90^\circ$, $SU = 13v$, $UT = 4v$

Step2: Calculate missing side $ST$

Use Pythagorean theorem: $ST = \sqrt{(SU)^2 - (UT)^2} = \sqrt{(13v)^2 - (4v)^2} = \sqrt{169v^2 - 16v^2} = \sqrt{153v^2} = 3\sqrt{17}v \approx 12.37v$

Step3: Compare side lengths

$13v > 3\sqrt{17}v > 4v$, so $SU$ is longest side.

Step4: Match side to opposite angle

Longest side $SU$ is opposite $\angle T$.

Answer:

$\angle T$