Answer:
Therefore, the values of x and y in the right-angled triangle are approximately x ≈ 10.39 and y = 6.
Step-by-step explanation:
To find the values of x and y in a right-angled triangle with the opposite side as 6 and the angle of 30 degrees, we can use trigonometric functions.
Given that the opposite side (y) is 6 and the angle is 30 degrees, we can use the sine function:
sin(30 degrees) = opposite/hypotenuse sin(30 degrees) = 6/hypotenuse
Since sin(30 degrees) = 1/2, we can substitute this value:
1/2 = 6/hypotenuse hypotenuse = 6 / (1/2) hypotenuse = 12
Now, we can use the Pythagorean theorem to find the third side (x):
x^2 = hypotenuse^2 - opposite^2 x^2 = 12^2 - 6^2 x^2 = 144 - 36 x^2 = 108 x = sqrt(108) x ≈ 10.39
Therefore, the values of x and y in the right-angled triangle are approximately x ≈ 10.39 and y = 6.