By using triangle properties and the law of the cosine twice, we find that the distance between points M and N is approximately 9.8 meters.
How to determine the distance between two points
In this problem we must determine the distance between two points that are part of a triangle and we can take advantage of properties of triangles to find it. First, we determine the measure of angle L by the law of the cosine:
[tex]\cos L = \frac{(19.6\,m)^{2}-(14.8\,m)^{2}-(21.4\,m)^{2}}{-2\cdot (14.8\,m)\cdot (21.4\,m)}[/tex]
L ≈ 62.464°
Then, we get the distance between points M and N by the law of the cosine once again:
[tex]MN = \sqrt{(7.4\,m)^{2}+(10.7\,m)^{2}-2\cdot (7.4\,m)\cdot (10.7\,m)\cdot \cos 62.464^{\circ}}[/tex]
MN ≈ 9.8 m
By using triangle properties and the law of the cosine twice, we find that the distance between points M and N is approximately 9.8 meters.
To learn more on triangles: https://brainly.com/question/2773823
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