Question

Given the figure, if XY = 12, what is the length of XZ

Answer 1

We have a right triangle.

As the other angles are equal, both with 45° measures, the legs have equal length too. Then, ZY = XZ.

We have to relate XY, the hypotenuse, with the leg XZ.

We can use the trigonometric ratio:

`\begin{gathered} \cos (45\degree)=\frac{\text{Opposite}}{\text{Hypotenuse}}=(XZ)/(XY) \\ XZ=XY\cdot\cos (45\degree) \\ XZ=12\cdot\frac{\sqrt[]{2}}{2} \\ XZ=6\sqrt[]{2} \end{gathered}`

Answer: XZ = 6√2