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The resultant of two forces acting on a body has a magnitude of 60 pounds. The angle between the 28-pound force and the resultant is 50°. Find the magnitude of the other force. a. 66.3 pounds b. 47.2 pounds c. 80.9 pounds d. 59.3 pounds 2.   Without the wind, a plane would fly due east at a rate of 150 mph. The wind is blowing southeast at a rate of 50 mph. The wind is blowing at a 45° angle from due east. How far off of the due east path does the wind blow the plane?  a. 5.3° b. 7.5° c. 10.8° d. 0.2°

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HomertheGenius
1.  We will use the Cosine Law:
x² = 60² + 28² - 2 · 60 · 28 · cos 50°
x² = 3,600 + 784 - 3360 · 0.6428
x² = 2,224.234
x = √2,224.234
x = 47.16 pounds ≈ 47.2
Answer: B ) 47.2 pounds
2. By the Cosine Law ( angle of 135° is opposite the forces resultant ):
R² = 150² + 50² - 2 · 150 · 50 · cos 135°
R² = 22,500+2,500 -15,000 · ( -0.71 )
R² = 35,650
R = √35,650 = 188.812 mph
After that we will use the Sine Law:
50 / sin α = 188.812 / sin 135°
50 / sin α = 188.812 / 0.71
sin α = 50 · 0.71 / 188.812
sin α = 0.188
α = sin^(-1) 0.188
α = 10.83° ≈ 10.8°
Answer: C ) 10.8° 

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