A ship is 90 miles south and 20 miles east of port. The captain wants to travel directly to port. What bearing should be taken?

A ship leaves port A and travels north for 47km and arrives at port B.It then travels east to port C which lies 35% of port A.How far is port C from port B? Draw a diagram to help you calculate.

Well, if the ship wants to go directly to port, it sounds like the captain should take a "seariously" good bearing! But in all seriousness, let's calculate it. Since the ship is 90 miles south and 20 miles east, we can use some trigonometry to figure out the bearing. The angle formed by the ship's position and the desired direction (towards port) can be found using the tangent function. The angle can be calculated as the arctan(20/90) which is approximately 12.68 degrees. So, the bearing the captain should take is approximately 12.68 degrees. And remember, always keep a "sea-sense" of humor on board!

To determine the bearing, we need to find the angle between the ship's current position and the direction towards port.

Let's draw a diagram to visualize the situation:

S (ship)
|\
| \
| \
| \
| \
| \
| \
| \
| \
P (port)

In this diagram, S represents the ship's current location and P represents the port. The ship is 90 miles south and 20 miles east of the port.

To find the bearing, we can use trigonometry. We will use the inverse tangent (arctan) function to calculate the angle. The arctan of the opposite side (east, 20 miles) divided by the adjacent side (south, 90 miles) will give us the angle.

So, the bearing can be calculated using the formula:

Bearing = arctan(opposite / adjacent)

Plugging in the values:

Bearing = arctan(20 / 90)

Using a calculator or a trigonometric table, we can find:

Bearing ≈ 12.39 degrees

So, the captain should take a bearing of approximately 12.39 degrees to head directly towards the port.

hi but

uiuhi

"90 miles south and 20 miles east of port"

means the direction along which the ship must sail is:
x=-90, y=20
angle = atan(20,-90) = 180° - 12°-31'-44"
= 167°-28'-16" (in trigonometry notation).

To convert trigonometry notation to bearing, subtract angle from 90° or 450° if the angle exceeds 90°.

Bearing (clockwise from north)
= 450° - 167°-28'-46"
= 282°-31'-44"