A light aircraft takes off flying due noth then turns and flies 11000 m due West. The plane then has a bearing 205 degrees from its starting point .For what distance did it fly due north
Huh?
205 is in the SOUTH west quadrant (180 is S, 270 is W). Either a typo or a pretty silly trick question.
To find the distance the aircraft flew due north, we need to break down the given information step by step.
1. The aircraft initially flies due north.
2. It then turns and flies due west for a distance of 11000 m.
3. Finally, it has a bearing of 205 degrees from its starting point.
Since the aircraft initially flew due north, we can assume that the distance it flew due north is equal to the total distance traveled minus the distance it traveled due west.
Let's calculate the distance it flew due north:
Total distance traveled = Distance due north + Distance due west
Since the distance due west is given as 11000 m, we need to determine the total distance traveled.
To find the total distance traveled, we can use trigonometry.
Using the given bearing of 205 degrees, we can calculate the angle between the direction of flight and due north:
Angle = 205 degrees - 180 degrees (since due north is 0 degrees)
Angle = 25 degrees
Now, we can use trigonometry to find the total distance traveled:
sin(25 degrees) = Distance due north / Total distance traveled
Rearranging the equation, we get:
Distance due north = sin(25 degrees) * Total distance traveled
Since sin(25 degrees) ≈ 0.4226, the distance due north can be calculated as:
Distance due north ≈ 0.4226 * Total distance traveled
Now, we just need to determine the total distance traveled. We can use the Pythagorean theorem to find it:
Total distance traveled ^ 2 = Distance due north ^ 2 + Distance due west ^ 2
Total distance traveled ^ 2 = (0.4226 * Total distance traveled) ^ 2 + 11000 m ^ 2
Simplifying the equation:
Total distance traveled ^ 2 = 0.1787 * Total distance traveled ^ 2 + 121,000,000 m ^ 2
0.8213 * Total distance traveled ^ 2 = 121,000,000 m ^ 2
Total distance traveled ^ 2 ≈ 121,000,000 m ^ 2 / 0.8213
Total distance traveled ^ 2 ≈ 147,250,902 m ^ 2
Taking the square root of both sides, we get:
Total distance traveled ≈ √147,250,902 m ^ 2
Total distance traveled ≈ 12135.8 m (rounded to one decimal place)
Therefore, the distance the aircraft flew due north is approximately:
Distance due north ≈ 0.4226 * 12135.8 m
Distance due north ≈ 5131.62 m (rounded to two decimal places)
Hence, the aircraft flew approximately 5131.62 meters (or 5.13 km) due north.
To find the distance the aircraft flew due north, we need to break down the given information and use trigonometry.
First, let's draw a diagram to visualize the situation. Assume the starting point as "O" and the final position as "P." The distance the aircraft flew due north can be represented as "OP."
```
N
^
|
|
O |
----> W
P
```
From the information provided, we know that the aircraft first flies due north and then turns to fly due west. Let's label the distance it flew due north as "x."
Now, we can use trigonometry to solve for "x."
Using the given information, we can deduce two right-angled triangles in the diagram:
1. The triangle ONP:
- The distance flown due west is 11000 m.
- The angle NOP is 205 degrees (measured clockwise from due north).
2. The triangle ONQ: (right-angled at Q)
- The distance flown due north is "x" m.
- The angle QNO is 360 - 205 = 155 degrees. (since the sum of the angles around a point is 360 degrees)
From trigonometry, we can use the tangent function to find the distance flown due north:
tan(angle) = opposite / adjacent
In the triangle ONQ:
tan(155) = x / 11000
To find "x," we can rearrange the equation as follows:
x = tan(155) * 11000
Now, we can calculate the value of "x."
Using a scientific calculator or an online trigonometry calculator, we find:
tan(155) ≈ 3.7321
Therefore, the distance flown due north "x" is approximately:
x ≈ 3.7321 * 11000 = 41,053.1 meters
Hence, the aircraft flew approximately 41,053.1 meters due north.