Question

use the law of cosines to find the value of cos. round your answer to two decimal places

Answer 1

The law of cosine says that

$10.9^2=5.8^2+10.5^2-2\times10.5\times5.8\cos\theta\implies\cos\theta\approx0.205911\approx0.21$

Answer 2

Answer:

A. 0.21

Step-by-step explanation:

We have been given a triangle and we are asked to find the value of cos using law of cosines.  

Law of cosines:

$c^2=a^2+b^2-2ab*cos(C)$

Upon substituting our given values in above formula we will get,

$10.9^2=5.8^2+10.5^2-2*5.8*10.5*cos(\theta)$

$118.81=33.64+110.25-121.8*cos(\theta)$

$118.81=143.89-121.8*cos(\theta)$

$118.81-143.89=143.89-143.89-121.8*cos(\theta)$

$-25.08=-121.8*cos(\theta)$

$\frac{-25.08}{-121.8}=\frac{-121.8*cos(\theta)}{-121.8}$

$0.2059113300492611=cos(\theta)$

Upon rounding our answer to nearest hundredth we will get,

$cos(\theta)\approx 0.21$

Therefore, the value of $cos(\theta)$ is 0.21 and option A is the correct choice.