a motor boat moves in the direction of N 38° E for 3 hrs at 20 mph. How far north and how far east does it travel?
I see a right-angled triangle with hypotenuse of 60 and a base angle of 52°
sin52 = y/60 --> y = 60sin52 = ...
cos52 = x/60 ---> x = 60cos52 = ...
Well, if the motor boat is moving in the direction of N 38° E, it means it's going slightly to the northeast. So, let's break it down:
If the boat is going at a constant speed of 20 mph for 3 hours, we can calculate the distance traveled by multiplying the speed by the time: 20 mph * 3 hours = 60 miles.
Now, to calculate how far north and how far east the boat traveled, we can use some trigonometry. Since the boat is moving slightly northeast, we can think of it as moving in two directions simultaneously - one north and one east.
If the boat is moving in the direction of N 38° E, it means it's moving 38 degrees away from the north direction. So, to find how far north it traveled, we can calculate the sine of 38 degrees multiplied by the distance traveled: sin(38°) * 60 miles = approximately 36.55 miles.
Similarly, the boat is moving in the direction of N 38° E, which means it's moving 52 degrees away from the east direction. So, to find how far east it traveled, we can calculate the cosine of 52 degrees multiplied by the distance traveled: cos(52°) * 60 miles = approximately 38.03 miles.
So, the motor boat traveled approximately 36.55 miles north and 38.03 miles east. Although, I hope it didn't end up swimming with the fishes!
To find out how far north and how far east the motor boat traveled, we can use the basic trigonometric relationships between the directions and distances.
Given:
Direction: N 38° E
Time: 3 hours
Speed: 20 mph
To determine the distance north (DN) and distance east (DE), we can use the formulas:
DN = Speed × sin(theta)
DE = Speed × cos(theta)
where theta is the angle between the direction and the north line (the angle formed by the north line and the direction line).
In this case, we need to determine the values of DN and DE.
Using trigonometric functions, we have:
DN = 20 × sin(38°)
DE = 20 × cos(38°)
Calculating:
DN = 20 × 0.6157 ≈ 12.314 miles
DE = 20 × 0.7880 ≈ 15.760 miles
Therefore, the motor boat traveled approximately 12.314 miles north and 15.760 miles east.
To find out how far north and east the motor boat travels, we can break down the given information:
1. The boat moves in the direction of N 38° E. This means that it is moving 38° east of north.
2. The boat travels at a speed of 20 mph for 3 hours.
To calculate how far the boat travels north and east, we can use trigonometry. We can consider the northward and eastward components of the boat's velocity separately.
Northward component:
The northward component can be calculated using the formula:
northward component = velocity x cos(angle)
Since the boat is moving 38° east of north, we can calculate the northward component as:
northward component = 20 mph x cos(38°)
Eastward component:
The eastward component can be calculated using the formula:
eastward component = velocity x sin(angle)
Since the boat is moving 38° east of north, we can calculate the eastward component as:
eastward component = 20 mph x sin(38°)
Now, let's calculate the northward and eastward components:
northward component = 20 mph x cos(38°)
eastward component = 20 mph x sin(38°)