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Papessa [141]
4 years ago
10

Solve the triangle.

Mathematics
1 answer:
Brrunno [24]4 years ago
5 0

Answer:

a ≈ 11.3, C ≈ 24.2, B ≈ 103.8

Step-by-step explanation:

The information A = 52°, b = 14, c = 6 lends itself to solution using the Law of Cosines:  a^2 = b^2 + c^2 - 2bc cos A.

Here, a^2 = 14^2 + 6^2 - 2(14)(6) cos 52 degrees, or

                 = 196 + 36 - 168 (0.616)

                  = 120.57

Taking the positive square root of this results in a = 11.3.

This corresponds to the second answer choice:  a ≈ 11.3, C ≈ 24.2, B ≈ 103.8

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Answer:

x = -4

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Step-by-step explanation:

Straight angles by definition have a total measure of 180°.

This means that m<LMP and m<NMP are 180° together.

Therefore m<LMP + m<NMP = 180°.

[substitution property]

(-16x + 13)° + (-20x + 23)° = 180°

[associative property of addition]

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_________________

Since m<LMP = (-16x + 13)°.

Using substitution with x = -4:

m<LMP = (-16(-4) + 13)° = (64 + 13)° = 77°.

Since m<NMP = (-20x + 23)°.

Using substitution with x = -4:

m<NMP = (-20(-4) + 23)° = (80 + 23)° = 103°.

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