Precal on plato
a plane is traveling due south. the wind is blowing 30° east of south at 50 miles/hour. if the plane's resultant speed due to the wind is 180 miles/hour, what is the plane's actual speed, rounded to the nearest integer?

120 miles/hour
130 miles/hour
135 miles/hour
140 miles/hour

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
C ) 135 miles/hour

C. 135 miles/hour

Step-by-step explanation: I got this right on Edmentum

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