A light air craft takes off flying die north then turns and flies 11 000 metres due west.The plane then has a bearing of 340 degrees from its starting point.For what distance did it fly due north?
the plane has a heading of 340°, not a bearing.
If they are heading toward a lighthouse on that heading, the lighthouse has a bearing of 340°
If the plane flies x meters due north, then
11000/x = tan 20°
x = 30222
30222
4, 003.7m
Well, if the light aircraft was flying due north, it probably should've invested in a better GPS system or asked for directions from Santa. But jokes aside, let's calculate the distance it flew due north.
To do that, we'll consider the right-angled triangle formed by the aircraft's flight path. The vertical side represents the distance it flew due north, the horizontal side represents the distance it flew due west (11,000 meters), and the hypotenuse represents the direct distance from the starting point to the ending point.
Now, we have the bearing of 340 degrees, which means we need to subtract that from a full circle (360 degrees) to get the angle inside the triangle. So, 360 - 340 = 20 degrees.
Using trigonometry, we can say that tan(20 degrees) = vertical side (distance due north) / horizontal side (11,000 meters).
By rearranging the formula, we get: vertical side = tan(20 degrees) * 11,000 meters.
Using a calculator, we find that tan(20 degrees) is approximately 0.3640.
Therefore, the distance the plane flew due north is approximately 0.3640 * 11,000 meters.
Calculating that, we find it flew approximately 4,004 meters due north.
So, to answer your question, it flew approximately 4,004 meters due north! Let's hope it didn't end up in the wrong hemisphere.
To find the distance the aircraft flew due north, we need to visualize the given information and use trigonometry. Here's how you can calculate it step by step:
1. Draw a diagram: Start by drawing a diagram of the aircraft's flight path. Label the starting point as "A" and the final destination as "B." Draw a vertical line representing the north direction and a horizontal line representing the west direction.
B
--------------------
| |
| | |
N| A |
| |
| |
--------------------
2. Determine the right-angled triangle: From the diagram, you can see that the aircraft's flight path forms a right-angled triangle. The line segment AB represents the hypotenuse, the vertical line represents the opposite side (north), and the horizontal line represents the adjacent side (west).
B
--------------------
| | 11,000 m
| | |
N| A |
| |
| |
--------------------
3. Apply trigonometric principles: Since we know the aircraft flew due west for 11,000 meters, we can consider the westward distance as the length of the adjacent side. The bearing of 340 degrees from the starting point means that the angle formed between the west direction and the hypotenuse is 340 degrees.
4. Use the cosine function: To find the length of the northward distance (opposite side), we can use the cosine function. The cosine of an angle is equal to the adjacent side divided by the hypotenuse. In this case, we have:
cos(angle) = adjacent side / hypotenuse (cos(340) = 11,000 / AB)
Rearranging the formula to solve for AB, we get:
AB = 11,000 / cos(340)
5. Calculate the distance: Use a calculator to find the value of cos(340) and then evaluate the division:
AB = 11,000 / cos(340)
AB ≈ 11,403.46 meters
Therefore, the aircraft flew approximately 11,403.46 meters due north.