The answer for the missing leg length (x) is 3√5.
*The hypotenuse is labeled as 3√10.
* One leg is labeled as 3√5.
* The other leg has an unknown length, labeled as x.
* There is a 45° angle at the vertex opposite the leg with length x.
Using trigonometry, we can find the missing side length (x) as follows:
1. Identify the relevant trigonometric ratio: Since we have a right angle and two side lengths, we can use the tangent function (tan). Tan is opposite over adjacent.
2. Set up the equation: In this case, x (opposite) is adjacent to the 45° angle, and 3√5 (adjacent) is opposite the 45° angle. Therefore, tan(45°) = x / 3√5.
3. Solve for x: Since tan(45°) = 1, we can rewrite the equation as x = 3√5 * tan(45°) = 3√5 * 1 = 3√5.
Therefore, the final answer for the missing leg length (x) is 3√5.