Find m∠c m .
a. 34
b. 57
c. 52
d. 64

  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.

answer: i'm not going to give you the answer, but some hints to work it out.

step-by-step explanation: so, if there is a straight line that means that the line angle is 180°. so we subtract the 2 angle measures provided, (15 and 38) from 180. so the answer is 180 - (38 + 15). (you have to solve the equation)

a) 32pie square meters

step-by-step explanation: