Final answer:
In both triangles, the sum of the angles is 180 degrees. We can use trigonometric ratios to find the lengths of the sides labeled x and y.
Step-by-step explanation:
In both triangles, the sum of the angles is 180 degrees. Therefore, in the first triangle with a 60 degree angle and a 40 degree angle, the remaining angle can be found by subtracting the sum of the given angles from 180 degrees: 180 - 60 - 40 = 80 degrees.
Next, we can use the trigonometric ratios to find the lengths of the sides labeled x and y. In the first triangle, we can use the sine ratio to find the length of side x:
sin(40°) = x / y
Cross-multiplying, we get:
x = y * sin(40°)
Similarly, in the second triangle, we can use the sine ratio to find the length of side y:
sin(80°) = y / x
Cross-multiplying, we get:
y = x * sin(80°)