Question

A farmer plants a 16-foot row of tomatoes 13-foot row of carrots and a 21-foot row of green peppers in a triangle find the angle formed by the tomatoes and carrots

Answer 1

The angle between tomatoes and carrots is 92.2°, approximately.

Explanation:

As you can observe in the image attached, the triangle formed is scalene, which means we need to use the law of cosines to find the answer.

`p^(2) =c^(2) +t^(2) -2(c)(t)(cos\theta)`

Where
`p` is green peppers,
`c` is carrots,
`t` is tomatoes and
`\theta` is the angle between tomatoes and carrtos.

Replacing all given values, we have

`21^(2) =13^(2) +16^(2) -2(13)(16)(cos\theta)\\441=169+256-416cos\theta\\441-169-256=-416cos\theta\\(16)/(-416)=cos\theta\\ \theta=cos^(-1)((1)/(-26) ) \approx 92.2\°`

Therefore, the angle between tomatoes and carrots is 92.2°, approximately.