Question

which equation correctly uses the law of cosines to solve for y? o 9² = y² + 19² - 2(y)(19)cos(41°) o y² = 9² + 19² - 2(y)(19)cos(41°) o 9² = y² + 19² - 2(9)(19)cos(41°) o y² = 9² + 19² - 2(9)(19)cos(41°) law of cosines: a² = b² + c² - 2bccos(a)

Explanation:

Step1: Identify sides and angle for law of cosines

In $\triangle XYZ$, we want to find $y$. Let $a = y$, $b = 9$, $c = 19$ and $A=41^{\circ}$.

Step2: Apply the law of cosines formula

The law of cosines is $a^{2}=b^{2}+c^{2}-2bc\cos(A)$. Substituting the values, we get $y^{2}=9^{2}+19^{2}-2(9)(19)\cos(41^{\circ})$.

Answer:

$y^{2}=9^{2}+19^{2}-2(9)(19)\cos(41^{\circ})$ (the fourth option)