A boat sails 50km on a bearing of 080 degree, calculate how far north it travels?
To calculate how far north the boat travels, we need to break down the direction it traveled in terms of its northward and eastward components.
First, we need to convert the bearing angle of 080 degrees to a standard mathematical angle. In a standard coordinate system, east corresponds to 0 degrees, north corresponds to 90 degrees, west corresponds to 180 degrees, and south corresponds to 270 degrees. Therefore, the bearing of 080 degrees corresponds to 10 degrees clockwise from due east.
Next, we can use trigonometry to calculate the northward and eastward components of the boat's distance traveled.
The northward component = 50km * sin(10 degrees)
The eastward component = 50km * cos(10 degrees)
Calculating the northward component:
northward component = 50km * sin(10 degrees)
northward component ≈ 8.66 km
Therefore, the boat travels approximately 8.66 km north.