Airplane navigation

An airplane leaves an airport and flies to west 120 miles and then 150 miles in the direction S 44.1°W. How far is the plane from the airport (round to the nearest mile)?

Correct result:

d =  251 nm

Solution:

x=120+150cos(44.1)=227.719 nm y=150sin(44.1)=104.387 nm  d2=x2+y2 d=227.7192+(104.387)2=251 nmx = 120+150 \cos(-44.1 ^\circ ) = 227.719 \ nm \ \\ y = 150 \sin(-44.1 ^\circ ) = -104.387 \ nm \ \\ \ \\ d^2 = x^2 + y^2 \ \\ d = \sqrt{ 227.719^2 + (-104.387)^2 } = 251 \ \text{nm}



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Tips to related online calculators
Two vectors given by its magnitudes and by included angle can be added by our vector sum calculator.
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Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

 
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