Answer:
![9](https://img.qammunity.org/2022/formulas/mathematics/college/b39gcp5k9dt6qk7hnkx2isvbviam8wxbyw.png)
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; (
), where (
) and (
) are the legs of the right triangle, or the sides adjacent to the right angle. (
) is the hypotenuse or the side opposite the right angle.
Substitute in the given values and solve, note that (
) represents the unknown leg (side).
![a^2 + b^2 = c^2\\\\a^2 + (√(19))^2 = (100)^2\\\\a^2 + 19 = 100](https://img.qammunity.org/2022/formulas/mathematics/college/8vwdmqrzqigzojgx10joabnhjtxnmgum9n.png)
Inverse operations,
![a^2 + 19 = 100\\-19\\\\a^2 = 81\\\\a = √(81)\\\\a = 9](https://img.qammunity.org/2022/formulas/mathematics/college/wy7ouubr8u3vm83y6z6cxgbt622qqcpzq6.png)