Final answer:
To find the length of XW in triangle XYZ, we can use the sine ratio and the given angles. By setting up the equation sin(∠X) = XY / XW, we can solve for XW. The length of XW is approximately 7.1.
Step-by-step explanation:
To find the length of XW in triangle XYZ, we can use the trigonometric ratios. Since we know that angle XWZ is a right angle, we can use the sine ratio to find the length of XW. The sine ratio is defined as the opposite side divided by the hypotenuse. In this case, the opposite side is XY and the hypotenuse is XW. Therefore, we can set up the equation sin(∠X) = XY / XW and solve for XW. Plugging in the given values, we have sin(59°) = 6.1 / XW. Solving for XW, we get XW ≈ 6.1 / sin(59°) ≈ 6.1 / 0.857 = 7.12.