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

Answer:

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

Step-by-step 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

$21^{2} =13^{2} +16^{2} -2(13)(16)(cos\theta)\\441=169+256-416cos\theta\\441-169-256=-416cos\theta\\\frac{16}{-416}=cos\theta\\ \theta=cos^{-1}(\frac{1}{-26} ) \approx 92.2\°$

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