We can use the Cosine Law:
c² = a² + b² - 2 ac cos C
180² = 50² + x² - 2 · 50 · x · cos 150°
32,400 = 2,500 + x ² - 100 x · ( - √3/2 )
32,400 - 2.500 - x² = 100 x · 0.866
29,900 - x² = 86.6 x
- x² - 86.6 x + 29,900 = 0 / · ( - 1 )
x² + 86.6 x - 29,900 = 0
x 1/2 = ( - 86.6 +/- √(86.6² + 4 · 1 · (-29,900) )) / 2
x = ( - 86.6 + 356.6 )/ 2 ( other solution is negative )
x = 135
Answer: C ) 135 miles/hour
