Let h be the length of the side opposite to 60°, and opposite to 45°
Using the trigonometric function tangent, we get the following:
[tex]\begin{gathered} \tan60°=\frac{\text{ opposite}}{\text{ adjacent}} \\ \\ \text{IF} \\ \text{opposite to }60°=h \\ \text{adjacent to }60°=y=3 \\ \\ \text{THEN} \\ \tan60°=\frac{h}{3} \\ h=3\tan60° \\ h=3\sqrt{3} \end{gathered}[/tex]
Now that we have x, we can now solve for segment x, using the same tangent function.
[tex]\begin{gathered} \tan45°=\frac{h}{x} \\ x=\frac{h}{\tan45°} \\ x=\frac{3\sqrt{3}}{1} \\ x=3\sqrt3 \\ \\ \text{Therefore, the measurement of }x\text{ is }3\sqrt{3} \end{gathered}[/tex]
