aqsafathima120710
Answered

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Archie is the captain of a ship.
There is a whirlpool 40 km due north of the ship.
There is a volcano due east of the whirlpool, at a bearing
of 058° from the ship.
Archie wants to sail in a straight line that passes through
the point halfway between the whirlpool and
the volcano
.
What bearing should he sail
on?
Give your answer to the nearest degree.
​

Sagot :

sqdancefan

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°.

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