Question

question 25 of 40 suppose a triangle has two sides of length 32 and 35, and that the angle between these two sides is 120°. which equation should you solve to find the length of the third side of the triangle? a. c = 32 + 35 - 2(32)(35)cos120° b. c² = 32² + 35² - 2(32)(35)cos120° c. c² = 32² + 35² - 2(32)(35)sin120° d. $\frac{sin32}{120}=\frac{sin35}{b}$

Explanation:

Step1: Recall the law of cosines

The law of cosines for a triangle with sides $a$, $b$, $c$ and the angle $\theta$ between sides $a$ and $b$ is $c^{2}=a^{2}+b^{2}-2ab\cos\theta$.

Step2: Identify values of $a$, $b$, $\theta$

Here $a = 32$, $b = 35$, and $\theta=120^{\circ}$.

Step3: Substitute values into law - of - cosines

Substituting into $c^{2}=a^{2}+b^{2}-2ab\cos\theta$, we get $c^{2}=32^{2}+35^{2}-2(32)(35)\cos120^{\circ}$.

Answer:

B. $c^{2}=32^{2}+35^{2}-2(32)(35)\cos120^{\circ}$