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Verizon [17]
2 years ago
6

Use the Law of Sines to find the missing angle of the triangle.

Mathematics
1 answer:
Natasha2012 [34]2 years ago
8 0

Answer:

m∠B = 70.0° (nearest tenth)

Step-by-step explanation:

<u>Sine Rule for Angles</u>

\sf \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}

(where A, B and C are the angles and a, b and c are the sides opposite the angles)

Given:

  • a = 13
  • c = 19
  • A = 40°

Substituting the given values into the formula to find m∠C:

\implies \sf \dfrac{\sin 40^{\circ}}{13}=\dfrac{\sin C}{19}

\implies \sf \sin C=\dfrac{19\sin 40^{\circ}}{13}

\implies \sf C=\sin^{-1}\left(\dfrac{19\sin 40^{\circ}}{13}\right)

\implies \sf m \angle C=69.96086904^{\circ}

Interior angles of a triangle sum to 180°

\implies \sf m \angle A+ m \angle B+m \angle C=180^{\circ}

\implies \sf 40^{\circ} + m \angle B+69.960...^{\circ}=180^{\circ}

\implies \sf m \angle B=70.03913...^{\circ}

Therefore, m∠B = 70.0° (nearest tenth)

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Two times x is 8 more than y. The sum of x and two times y is 14. Write two equations and graph to find the value of y.
Sauron [17]

Option B: $y=4$ is the value of y

Explanation:

It is given that "Two times x is 8 more than y". Writing it as expression, we have,

2x=8+y

It is also given that "The sum of x and two times y is 14". Writing it as expression, we have,

x+2y=14

To find the value of y, let us solve the two equations using substitution method.

From the equation 2x=8+y , let us find the value of x.

x=\frac{8+y}{2}

x=\frac{8}{2} +\frac{y}{2}

x=4+\frac{y}{2}

Now, substituting x=4+\frac{y}{2} in the equation x+2y=14 , we get,

4+\frac{y}{2}+2y=14

      4+\frac{5y}{2} =14

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            5y=20

              $y=4$

Thus, the value of y is $y=4$

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Step-by-step explanation:

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