A ship sails 50 km on a bearing of 70 degrees. How far North is it from its starting position.
Assuming that "bearing" to you means North = 0 and you are going clockwise.
Make a sketch and complete the right-angled triangle:
sin20° = y/50 ---> y = 50sin20 = appr 17.1 km
or
cos70° = y/50 ---> y = 50cos70 = appr 17.1 km
Well, I guess you could say the ship went on a little adventure! If the ship sailed 50 km on a bearing of 70 degrees, let's break out our compasses and calculate its northern displacement.
To find out how far north the ship is from its starting position, we need to use some trigonometry. The bearing of 70 degrees is measured clockwise from the north.
Now, if we take the sine of 70 degrees, we'll get the ratio of the vertical displacement to the total displacement. In this case, it'll give us the distance north.
So, sin(70 degrees) ≈ 0.9397.
Finally, we multiply this by the distance the ship traveled, which is 50 km.
0.9397 * 50 km ≈ 46.98 km.
Therefore, the ship is approximately 46.98 km north of its starting position.
Just remember, instead of asking the ship for directions, you might want to consider getting a GPS next time. It's a bit more reliable and less prone to exploring unexpected fishing trips!
To find how far North the ship is from its starting position, we need to calculate the Northward component of its journey.
Step 1: Identify the Northward component.
To do this, we will use some trigonometry. We know the ship sailed on a bearing of 70 degrees, which means the ship moved in a direction 70 degrees clockwise from the North.
Step 2: Find the Northward component using trigonometry.
The Northward (N) component can be calculated using the formula: N = distance x sin(angle).
Angle = 70 degrees and distance = 50 km.
N = 50 km x sin(70 degrees).
Using a calculator, we calculate N ≈ 44.59 km.
Therefore, the ship is approximately 44.59 km North of its starting position.
To determine how far north the ship is from its starting position, we need to analyze the given information.
First, let's visualize the situation. Imagine a map with the starting position of the ship as a reference point. We need to determine how much the ship has moved vertically (northwards or southwards) from this reference point.
Now, let's break down the information provided. The ship has sailed 50 km on a bearing of 70 degrees.
A bearing angle represents the direction in which an object is facing or moving, using degrees measured clockwise from true north. In this case, a bearing of 70 degrees means the ship is moving 70 degrees towards the east (clockwise) from true north.
To determine the distance the ship traveled vertically northwards, we need to use trigonometry.
Since the bearing angle (70 degrees) is measured clockwise from the reference direction (true north), we can refer to the angle counterclockwise from the north as the complement angle (90 - 70 = 20 degrees).
Now, we can use trigonometric ratios, specifically the sine function, to calculate the vertical displacement (distance northwards):
sin(20 degrees) = Opposite / Hypotenuse
The hypotenuse represents the total distance traveled by the ship, which is given as 50 km. Therefore:
sin(20 degrees) = Opposite / 50 km
To isolate the Opposite (which represents the distance northwards), multiply both sides of the equation by 50 km:
Opposite = 50 km * sin(20 degrees)
Using a scientific calculator, we can evaluate the sine of 20 degrees, which is approximately 0.3420:
Opposite = 50 km * 0.3420
Calculating:
Opposite ≈ 17.10 km
Therefore, the ship is approximately 17.10 km north of its starting position.