Velocity of Plane Relative to Ground: Answer & Explanation

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A plane traveling east at 210 km/hr encounters a southward wind at 85 km/hr, resulting in a ground velocity of 227 km/hr. The calculated angle using the tangent function indicates a direction of 22 degrees. The confusion arises regarding whether this angle is measured south of east or east of south. The correct interpretation is that the angle signifies 22 degrees south of east. Thus, the final answer is 227 km/hr at an angle of 22 degrees south of east.
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A plane is headed eastward at a speed of 210 km/hr. The wind is blowing southward at 85.0 km/hr. The velocity of the plane relative to the ground is?
a. 192 km/hr at an angle of 22 degrees south of east
b. 192 km/hr at an angle of 22 degrees east of south
c. 227 km/hr at an angle of 68 degrees south of east
d. 227 km/hr at an angle of 68 degrees east of south

For the velocity, I did square root (210^2 + 85.0^2) and I got 227 km/hr. However, when finding the angle, I did tan-1(85/210) and got 22 degrees. I don't know which one would be the correct answer then.
 
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First tell me,

Which direction does tan-1(85/225) signify-
east of south or south of east?

The answer to your question lies in this particular answer!
 
Hi,

Agree with you.. please justify the direction..
 
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