10 POINTS!!! Label the sides of the triangle (a, b, and c). Use the Law of Cosines and the Law of Sines to solve the triangle. Round your answer to the nearest whole number.

  c = 29, A = 48°, B = 54°

Step-by-step explanation:

The unknown side is c. Using the last Law of Cosines formula, we find it to be ...

  c² = a² +b² -2ab·cos(C)

  c² = 22² +24² -2(22)(24)cos(78°) ≈ 840.445

  c ≈ √840.445 ≈ 29 . . . . . rounded to integer

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The angle at B can be found using the Law of Sines. We want the angle in the numerator, so we can write the equation as ...

  sin(B)/b = sin(C)/c

  B = arcsin(b/c·sin(C)) ≈ arcsin(24/28.9904×sin(78°))

  B ≈ 54°

The remaining angle can be found using the sum of angles of a triangle:

  A +B +C = 180°

  A = 180° -B -C = 180° -54° -78° = 48°

The solution to the triangle is ...

  c = 29, A = 48°, B = 54°

dilation scale factor 2: starting with δabc, draw the dilation image of the triangle with a center at the origin and a scale factor of two. notice that every coordinate of the original triangle has been multiplied by the scale factor (x2). dilation with scale factor 2, multiply by 2.