Answer:
039°
Step-by-step explanation:
You want the bearing of a point that is halfway between 40 km due north and a point due east of that on a bearing of 58°.
Tangent
The distance east of the whirlpool can be found using the tangent relation:
Tan = Opposite/Adjacent
tan(58°) = (east distance)/(40 km) . . . . substitute given values
east distance = (40 km)·tan(58°)
Target
The point for which we are aiming is half this distance east of the whirlpool. The angle can be found using the same relation:
[tex]\tan(\text{bearing})=\dfrac{\dfrac{1}{2}\cdot\text{east distance}}{40\text{ km}}=\dfrac{(40\text{ km})\tan(58^\circ)}{2\cdot(40\text{ km})}\\\\\\\text{bearing}=\arctan\left(\dfrac{\tan(58^\circ)}{2}\right)\approx 38.7^\circ[/tex]
The captain should sail on a bearing of about 39°.
