Answer:
[tex]9[/tex]
Step-by-step explanation:
As per the problem, the given triangle is a right triangle. This is signified by the box around one of its angles, this box states that the angle it is surrounding is a right angle.
Since it is a right triangle, one can use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that; ([tex]a^2 + b^2 = c^2[/tex]), where ([tex]a[/tex]) and ([tex]b[/tex]) are the legs of the right triangle, or the sides adjacent to the right angle. ([tex]c[/tex]) is the hypotenuse or the side opposite the right angle.
Substitute in the given values and solve, note that ([tex]a[/tex]) represents the unknown leg (side).
[tex]a^2 + b^2 = c^2\\\\a^2 + (\sqrt{19})^2 = (100)^2\\\\a^2 + 19 = 100[/tex]
Inverse operations,
[tex]a^2 + 19 = 100\\-19\\\\a^2 = 81\\\\a = \sqrt{81}\\\\a = 9[/tex]
