to go from town a to b a plane must fly about 1780km at an angle 30° west of north . how far north of A is B ?
Cos30 = d/1780, d = ?.
Gud
To determine how far north of town A is town B, we need to use trigonometry. Given that the plane flies at an angle of 30 degrees west of north and travels a distance of 1780 km, we can find the northward component of the plane's displacement.
Step 1: Determine the northward component of the plane's displacement.
To find the northward component, we can use the sine function since the angle is given. The formula for the northward component is:
Northward Component = Distance Traveled × sin(Angle)
Northward Component = 1780 km × sin(30°)
Using the sine function of 30 degrees (which is 0.5):
Northward Component = 1780 km × 0.5
Northward Component = 890 km
Therefore, town B is located 890 km north of town A.
To find the distance north of town A to town B, you can use trigonometry.
First, let's break down the given information:
- The plane has to fly 1780 km.
- The angle of 30° west of north suggests that the plane's path is deviating 30° to the west from the north direction.
Now, let's calculate the northward distance traveled by the plane. We can use trigonometric functions, specifically sine and cosine.
Step 1: Apply cosine function to find the westward distance (x):
cos(30°) = adjacent/hypotenuse
cos(30°) = x/1780 km
Step 2: Solve for x:
x = cos(30°) * 1780 km
Step 3: Apply sine function to find the northward distance (y):
sin(30°) = opposite/hypotenuse
sin(30°) = y/1780 km
Step 4: Solve for y:
y = sin(30°) * 1780 km
Therefore, the distance north of town A is y = sin(30°) * 1780 km.
Now, let's calculate the value:
y = sin(30°) * 1780 km
y = 0.5 * 1780 km
y = 0.5 * 1780 km = 890 km
Hence, town B is located approximately 890 km north of town A.