Question

Find m∠C m . A. 34 B. 57 C. 52 D. 64

Answer 1

Answer:

  B.  57

Step-by-step explanation:

You can solve the triangle using the Law of Cosines, then find the required angle using the Law of Sines. Or, you can estimate it based on the fact that the angle shown is very nearly 90°.

If ∠B were 90°, then the value of ∠C would be ...

  ∠C ≈ arctan(21/14) ≈ arctan(1.5) ≈ 56.3°

Since ∠B is slightly smaller, ∠C will be slightly larger. The nearest value slightly larger than 56.3° is choice B, 57°.

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Doing this the long way, you get ...

  b² = a² + c² - 2ac·cos(B) = 14² +21² -2(14)(21)cos(89°) ≈ 626.738

  b ≈ √626.738 ≈ 25.035

Then angle C is given by the law of sines as ...

  sin(C)/c = sin(B)/b

  C = arcsin(c/b·sin(B)) ≈ arcsin(0.838707) ≈ 57.004°

  m∠C ≈ 57°

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Many graphing calculators can solve triangles, as can phone or tablet apps.