Because of the wind, a boat sails 4,728 meters in the direction S 47deg29mins W. How far south it goes? How far west has it gone?
sin 47 degree 29 minutes = x/4728
x=4728(sin 47 degrees 29 minutes)
x=3484.92m
cos 47 degree 29 minutes= y / 4728
y= 4728(cos 47 degrees 29 minutes)
y= 3195.20 m
Am i correct?
Youre correct
To determine how far south the boat has gone, we need to find the component of the distance in the south direction.
Given that the direction is S 47°29' W, we can break it down into its components:
South component = Distance × sin(S 47°29' W)
West component = Distance × cos(S 47°29' W)
First, let's convert the angle to decimal degrees.
Angle in decimal degrees = 47 + (29/60) = 47.4833°
Now, we can calculate the components:
South component = 4,728 meters × sin(47.4833°)
West component = 4,728 meters × cos(47.4833°)
Calculating the south and west components:
South component = 4,728 × sin(47.4833°) ≈ 3,313 meters
West component = 4,728 × cos(47.4833°) ≈ 3,020 meters
Therefore, the boat has gone approximately 3,313 meters south and 3,020 meters west.
To determine how far south the boat goes and how far west it has gone, we need to break down the given direction into its components: south and west.
In the given direction, S 47°29' W, the first part, "S" indicates the boat is moving south, and the second part, "47°29' W" indicates the boat is moving 47 degrees and 29 minutes westward.
To find the southward distance:
- Take the given total distance traveled, which is 4,728 meters.
- Multiply it by the sine of the angle 47°29', as the sine function gives the ratio of the opposite side to the hypotenuse in a right-angled triangle. In this case, the opposite side represents the southward distance and the hypotenuse represents the total distance traveled.
- The formula for finding the opposite side length (southward distance) is: Opposite side length = Total distance * sin(angle).
Now, let's calculate the southward distance:
Southward distance = 4,728 meters * sin(47°29')
To find the westward distance:
- Similar to the calculation for the southward distance, we will multiply the total distance traveled by the cosine of the angle 47°29', since the cosine function gives the ratio of the adjacent side to the hypotenuse in a right-angled triangle. In this case, the adjacent side represents the westward distance and the hypotenuse represents the total distance traveled.
- The formula for finding the adjacent side length (westward distance) is: Adjacent side length = Total distance * cos(angle).
Now, let's calculate the westward distance:
Westward distance = 4,728 meters * cos(47°29')
By plugging these values into a scientific calculator or using trigonometric tables, we can find the precise southward and westward distances traveled by the boat.