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*10.5*5.8\cos\theta\implies\cos\theta\approx0.205911\approx0.21`

Answer 2

A. 0.21

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)`

`(-25.08)/(-121.8)=(-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.