Question

If segment y measures 3 what is the length of segment x?

Answer 1

Let h be the length of the side opposite to 60°, and opposite to 45°

Using the trigonometric function tangent, we get the following:

`\begin{gathered} \tan60°=\frac{\text{ opposite}}{\text{ adjacent}} \\ \\ \text{IF} \\ \text{opposite to }60°=h \\ \text{adjacent to }60°=y=3 \\ \\ \text{THEN} \\ \tan60°=(h)/(3) \\ h=3\tan60° \\ h=3√(3) \end{gathered}`

Now that we have x, we can now solve for segment x, using the same tangent function.

`\begin{gathered} \tan45°=(h)/(x) \\ x=(h)/(\tan45°) \\ x=(3√(3))/(1) \\ x=3\sqrt3 \\ \\ \text{Therefore, the measurement of }x\text{ is }3√(3) \end{gathered}`