Answer:
The correct answer is A. x = 15, y = 15√3
Explanation:
1. Let's solve for y, using the Law of the Cosines, this way:
We have the Δ ABC with m ∠B= 120° and AB and BC = 30
AC ² = 30² + 30² - 2 * 30 * 30 * Cos 120°
AC ² = 900 + 900 + 2 * 30 * 30 * - 0.5
AC ² = 1,800 + 900
AC ² = 2,700
AC = √2,700
AC = √900 * 3
AC = 30 √3
y = AC/2 = 30√3/2 = 15√3
2. Let's solve for x, using the Pythagorean theorem, this way:
x² = 30² - (15√3)²
x² = 900 - (225 * 3)
x² = 900 - 675
x² = 225
x = √225 = 15
The correct answer is A. x = 15, y = 15√3