A ship sails 50km on a bearing of 080 degrees calculate how far east it travels to the nearest tenth
if you want the eastward displacement ...
x/50 = cos 10°
x = .....
Well, to calculate how far east the ship travels, we need to use some basic trigonometry. But before I do that, let me ask you this: Did the ship remember to bring a GPS, or are they still using a compass and sextant? Because if they're using the latter, they might end up in the land of pirate ghosts and mermaid ninjas!
To calculate how far east the ship travels, we can use trigonometry.
Step 1: Convert the bearing to a mathematical angle.
The bearing of 080 degrees can be converted to a mathematical angle by subtracting it from 90 degrees because the reference angle for the east direction is 90 degrees.
90 degrees - 80 degrees = 10 degrees
Step 2: Use trigonometry to find the eastward distance.
The eastward distance can be found using the sine function:
Eastward distance = Total distance * sin(angle)
Given that the total distance sailed is 50 km and the angle is 10 degrees, we can calculate:
Eastward distance = 50 km * sin(10 degrees)
Using a calculator, the sine of 10 degrees is approximately 0.1736.
Eastward distance = 50 km * 0.1736
Eastward distance = 8.68 km (rounded to the nearest tenth)
Therefore, the ship travels approximately 8.68 km east.
To calculate how far east the ship travels, we need to use trigonometry.
The bearing of 080 degrees means that the ship is traveling clockwise from the north direction.
We can break down the distance traveled into the north and east components using trigonometric functions. The north component can be found using the sine function, and the east component can be found using the cosine function.
To find the east component:
1. Convert the bearing angle from degrees to radians. To convert degrees to radians, multiply the bearing angle by π/180.
080 degrees * π/180 = 4π/9 radians (rounded to the nearest thousandth)
2. Use the cosine function to find the east component.
east component = distance * cos(bearing angle in radians)
east component = 50 km * cos(4π/9)
east component ≈ 50 km * 0.766 = 38.3 km (rounded to the nearest tenth)
Therefore, the ship travels approximately 38.3 km east.