Question

Help please quickly!!!!!!1

Answer 1

Answer:

$9$

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; ($a^2 + b^2 = c^2$), where ($a$) and ($b$) are the legs of the right triangle, or the sides adjacent to the right angle. ($c$) is the hypotenuse or the side opposite the right angle.

Substitute in the given values and solve, note that ($a$) represents the unknown leg (side).

$a^2 + b^2 = c^2\\\\a^2 + (\sqrt{19})^2 = (100)^2\\\\a^2 + 19 = 100$

Inverse operations,

$a^2 + 19 = 100\\-19\\\\a^2 = 81\\\\a = \sqrt{81}\\\\a = 9$