Bearing - navigation

A ship travels 84 km on a bearing of 17°, and then travels on a bearing of 107° for 135 km. Find the distance of the end of the trip from the starting point, to the nearest kilometer.

Result

x =  159 km

Solution:

u=(84cos17;84sin17)=(80.33;24.559) v=(135cos107;135sin107)=(39.47;129.101) x=u+v=(80.33+(39.47))2+(24.559+129.101)2=159 km u = (84 \cdot \cos 17; 84 \cdot \sin 17) = (80.33; 24.559) \ \\ v = (135 \cdot \cos 107; 135 \cdot \sin 107) = (-39.47; 129.101) \ \\ x=|u+v| = \sqrt{ (80.33+(-39.47))^2+ (24.559+129.101)^2 } = 159 \ \text{km} \ \\



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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.
See also our trigonometric triangle calculator.
Pythagorean theorem is the base for the right triangle calculator.

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