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a. 78

b. 83

c. 86

d. 80

a 78 b 83 c 86 d 80

Answer :

The angle between the two kayakers is given as follows:

83º.

How to obtain the angle between two vectors?

The cosine of the angle between two vectors a and b is obtained according to the equation presented as follows:

[tex]\cos{\theta} = \frac{ab}{|a||b|}[/tex]

In which:

  • ab is the dot product of vectors a and b.
  • |a| is the norm of vector a.
  • |b| is the norm of vector b.

The dot product of the two vectors in this problem is given as follows:

190 x 128 - 160 x 121 = 4960.

The norm of each vector is given as follows:

  • |a| = sqrt(190² + 160²) = 248.4.
  • |b| = sqrt(128² + 121²) = 176.1.

Hence the angle is obtained as follows:

cos(x) = 4960/(248.4 x 176.1)

cos(x) = 0.1134

x = arccos(0.1134)

x = 83º.

More can be learned about the angle between two vectors at https://brainly.com/question/25705666

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