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wolf1728
We'll use the Law of Cosines and call
Angle M angle A
Angle N angle B and
Angle P angle C
Side m = 13 feet = side a
Side n = 10 feet = side b
Side p = side c
c^2 = a^2 + b^2 -2ab * cos C
c^2 = 13^2 + 10^2 -2*13*10 * cos(78)
c^2 = 169 + 100 - (260 * 0.20791)
c^2 = 269 - 54.0566
c^2 = 214.9434
c = 14.6609481276
answer is b









Ver imagen wolf1728
MrRoyal

The length of the side MN is 14.7 ft

The given parameters are:

MP = 10 ft

PN = 13 ft

Angle P = 78 degrees

To determine the length MN, we make use of the following cosine law

[tex]c^2 = a^2 + b^2 -2ab * cos C[/tex]

So, we have:

[tex]c^2 = 13^2 + 10^2 -2*13*10 * cos(78)[/tex]

Evaluate the exponents, and the products

[tex]c^2 = 169 + 100 - (260 * 0.20791)[/tex]

Evaluate the sum and the product

[tex]c^2 = 269 - 54.0566[/tex]

Evaluate the difference

[tex]c^2 = 214.9434[/tex]

Take the square root of both sides

[tex]c = 14.6609481276[/tex]

Approximate

[tex]c = 14.7[/tex]

Hence, the length of the side MN is 14.7 ft

Read more about law of cosines at:

https://brainly.com/question/4372174

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