Find x and y.

a. x = 15, y = 15root3

b. x = 15root3, y = 15

c. x = 30root3, y = 30

d. x = 30, y = 30root3

The correct answer is A. x = 15, y = 15√3

Step-by-step 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

answer: two angles are called supplementary if they add up to 180°. example: the two angles (140° and 40°) are supplementary because they add up to 180°.

step-by-step explanation: