Question

question 1 of 25
use the law of cosines to find the value of cosθ. round your answer to two decimal places.
a. 0.22
b. 0.84
c. -1.04
d. 0.35

Explanation:

Step1: Recall law of cosines formula

$c^{2}=a^{2}+b^{2}-2ab\cos\theta$, where $c = 10.2$, $a = 6.7$, $b = 9.8$. Rearrange for $\cos\theta$: $\cos\theta=\frac{a^{2}+b^{2}-c^{2}}{2ab}$.

Step2: Substitute values

$a^{2}=6.7^{2}=44.89$, $b^{2}=9.8^{2}=96.04$, $c^{2}=10.2^{2}=104.04$. Then $a^{2}+b^{2}-c^{2}=44.89 + 96.04-104.04=36.89$. And $2ab=2\times6.7\times9.8 = 131.32$.

Step3: Calculate $\cos\theta$

$\cos\theta=\frac{36.89}{131.32}\approx0.35$.

Answer:

D. 0.35