To determine the missing side lengths we need first notice that this is a right triangle; we also notice that we know and angle and its adjecent leg.
Now, u is the hypotenuse of the triangle; to determine it we can use the cosine function which is defined as:
[tex]\cos\theta=\frac{adj}{hyp}[/tex]
In this case we know that the angle is 60° and the adjecent leg is 13; then we have:
[tex]\begin{gathered} \cos60=\frac{13}{u} \\ u=\frac{13}{\cos60} \\ u=\frac{13}{\frac{1}{2}} \\ u=26 \end{gathered}[/tex]
Now, to determine the remaining length, v, we can use the pythagorean theorem which states that:
[tex]c^2=a^2+b^2[/tex]
where a and b are the legs and c is the hypotenuse.
In this case the hypotenuse is 26 and one of the legs is 13, then we have:
[tex]\begin{gathered} 26^2=v^2+13^2 \\ v^2=26^2-13^2 \\ v^2=507 \\ v=\sqrt{507} \end{gathered}[/tex]
Therefore, we conclude that:
[tex]\begin{gathered} u=26 \\ v=\sqrt{507} \end{gathered}[/tex]
