Given a side and an angle of a right triangle, to find the other side (TU), follow the steps.
Step 1: Use the function of tangent.
[tex]\tan (x)=\frac{\text{opposite}}{\text{adjacent}}[/tex]
Step 2: Find the opposite and adjacent sides to 34°.
The opposite side is TU;
The adjacent side is ST = 6.
Step 3: Substitute the values in the equation.
[tex]\tan (34)=\frac{TU}{6}[/tex]
Step 4: Multiply both sides by 6 to isolate TU.
[tex]\begin{gathered} 6\cdot\tan (34)+\frac{6}{6}TU \\ TU=6\cdot\tan (34) \end{gathered}[/tex]
Step 5: Find tan(34) and multiply by 6.
[tex]\begin{gathered} TU=6\cdot0.674 \\ TU=4 \end{gathered}[/tex]
Answer: TU = 4.
