Answer:
#1
Sum of interior angles is 180:
- y = 180 - (42 + 31) = 107
The law of sines:
- x / sin 107 = 11 / sin 42
- x = 11 sin 107deg / sin 42deg
- x = 15.72
#2
The law of cosines:
- cos 76 = (6² + 17² - x² )/2(6)(17)
- 204*0.24 = 325 - x²
- x² = 325 - 48.96
- x² = 276.04
- x = √276.04
- x = 16.61
#3
Same as above:
- 2*9.4*10*cos 20 = (10² + 9.4² - x²)
- 176.66 = 188.36 - x²
- x² = 188.36 - 176.66
- x² = 11.7
- x = √11.7
- x = 3.42
#4
Sum of interior angles is 180:
The law of sines:
- x / sin 34 = 15 / sin 94
- x = 15 sin 34 / sin 94
- x = 8.41