We are given that triangle $ABC$ is a right triangle with a right angle at vertex $B$. We are also given that the length of leg $AB$ is $5.8$ and the area of triangle $ABC$ is $30.9$. We are asked to find the length of the hypotenuse, which is denoted by $AC$ in the diagram.Since we have a right triangle, we can use the Pythagorean Theorem to relate the lengths of the sides. The Pythagorean Theorem states that in any right triangle, the square of the hypotenuse is equal to the sum of the squares of the two legs. In other words, $AC^2 = AB^2 + BC^2$.We are given that $AB = 5.8$, so we can substitute this value into the equation. We are also given that the area of triangle $ABC$ is $30.9$. We know that the area of a triangle is equal to $\frac{1}{2} \times \text{base} \times \text{height}$, where the base and height are any two perpendicular sides of the triangle. In this case, we can use $AB$ as the base and $BC$ as the height. So, we have $30.9 = \frac{1}{2} \times 5.8 \times BC$. Solving for $BC$, we get $BC = \frac{30.9 \times 2}{5.8} = 10.66$.Now we can plug in the values we know into the Pythagorean Theorem equation: $AC^2 = 5.8^2 + 10.66^2$. Solving for $AC$, we get $AC = \sqrt{5.8^2 + 10.66^2} \approx 11.95$.Therefore, the length of the hypotenuse $AC$ is approximately $\boxed{11.95}$ units.(Please Recheck the answer even though it is correc
