We need to find the value of x for the triangle:
Notice that this triangle has a right angle (90º), which is represented by the square marking.
Also, it has two congruent angles, which are represented by the same markings.
Since the internal angles of a triangle must add up to 180º, those acute angles measure 45º each:
[tex]90\degree+45\degree+45\degree=180\degree[/tex]
Now, for this 45-45-90 triangle, we have:
[tex]\frac{\text{ opposite leg}}{\text{ hypotenuse}}=\frac{\text{ adjacent leg}}{\text{ hypotenuse}}=\frac{1}{\sqrt{2}}[/tex]
Thus, we have:
[tex]\begin{gathered} \frac{x}{\sqrt{10}}=\frac{1}{\sqrt{2}} \\ \\ \frac{\sqrt{10}}{\sqrt{10}}x=\frac{\sqrt{10}}{\sqrt{2}} \\ \\ x=\frac{\sqrt{2}\cdot\sqrt{5}}{\sqrt{2}} \\ \\ x=\sqrt{5} \end{gathered}[/tex]
Answer:
[tex]x=\sqrt{5}[/tex]
