Question

A ship sails on a bearing of 020° for 30 km.
Find how far East the ship is from his starting position.
Give your answer correct to 1 decimal place.

Answer 1

Answer:

The ship travels approximately 10.261 meters to the East.

Step-by-step explanation:

At first we introduce a graphical description of the statement as an attachment below. Let suppose that bearing is respect to the North-direction, then the change in position in the East direction is modelled by the following Trigonometric formula:

$x = r\cdot \sin \theta$ (1)

Where:

$r$ - Distance travelled by the ship, measured in kilometers.

$\theta$ - Bearing angle, measured in sexagesimal degrees.

$x$ - Distance component in the east direction, measured in kilometers.

If we know that $r = 30\,km$ and $\theta = 20^{\circ}$, then the distance in the East direction is:

$x = (30\,km)\cdot \sin 20^{\circ}$

$x \approx 10.261\,m$

The ship travels approximately 10.261 meters to the East.

Answer 2

The bearing is the angle measured relative to or from the Northern

direction.

The ship's distance East from its starting point is approximately 10.26 km.

Reasons:

The given bearing of the ship's path, θ = 020°

The distance the ship has travelled = 30 km.

Required:

The ship's distance East from its starting position

Solution:

By using trigonometric ratios, we have;

$sin(\theta) = \dfrac{Ship's \ distance \ East \ from \ its \ starting \ point}{The \ distance \ the \ ship \ has \ sailed}$

Which gives;

$sin(20^{\circ}) = \dfrac{Ship's \ distance \ East \ from \ its \ starting \ point}{30 \ km}$

• The ship's distance East from its starting point = 30 km × sin(20°) ≈ 10.26 km.

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