Question

Need help on 1-6 please I need to solve for x and I need to get this done.

Answer 1

1-3 are about trigonometric ratios (SOH CAH TOA). 4, 5 are about the Law of Cosines, and 6 uses the Law of Sines.

1. Sin = Opposite/Hypotenuse
  x = 10*sin(40°) ≈ 6.428

2. Sin = Opposite/Hypotenuse
  x = arcsin(7/12) ≈ 35.69°

3. Tan = Opposite/Adjacent
  x = 18/tan(52°) ≈ 14.063

4. b^2 = a^2 +c^2 -2ac*cos(B)
  B = arccos((a^2 +c^2 -b^2)/(2ac)) = arccos((7^2 +13^2 -8^2)/(2*7*13))
  B = arccos(11/13) ≈32.20°

5. Same formula.
  x = √(a^2 +c^2 -2ab*cos(B)) = √(157-132cos(42°)) ≈ 7.675

6. The ratio of side lengths is the same as the ratio of the sines of the opposite angles.
  6/10 = sin(x)/sin(100°)
  x = arcsin((6/10)*sin(100°)) ≈ 36.22°