A plane leaves point A and flies S80° E to point B400 km away. How far east of A is B (to the nearest kilometer)?
Draw this on a graph. Put point A on the positive y-axis. From A, draw a line that looks to represent 80 degrees, to the x-axis at point B.
The distance from the origin to B is what you want to find.
In that right triangle with right angle at the origin, sin 80 degrees = x/400. Solve for x.
To find the distance east of point A to point B, you will need to use trigonometry and the given information. Here's how you can calculate it:
1. Draw a diagram: Draw a line segment to represent the distance between point A and point B. Label point A as the starting point, and point B as the ending point. The line segment between A and B represents the 400 km distance.
A --------- 400 km --------- B
2. Identify the angle: The angle between the line segment AB and due East is given as S80° E. The "S" refers to the South direction, which means the angle is measured from the South direction to the East direction.
3. Calculate the angle: To find the angle between the line segment AB and the East direction, subtract the given angle from 90° (since it is measured from the South direction). Therefore, 90° - 80° = 10°.
4. Find the distance east: Now, determine the distance east of A to B using trigonometry. Since we have an angle and the hypotenuse (400 km), we can use the cosine function. The cosine function is defined as the adjacent side divided by the hypotenuse.
Cos(angle) = Adjacent / Hypotenuse
Since the adjacent side represents the distance east of point A to point B, we can rewrite the formula as:
Cos(10°) = Adjacent / 400 km
Rearranging the equation to solve for the adjacent side (distance east):
Adjacent = Cos(10°) * 400 km
5. Calculate the distance east: Use a scientific calculator or online calculator to find the cosine of 10°, and then multiply it by 400 km.
Cos(10°) ≈ 0.9848
Distance east = 0.9848 * 400 km
Distance east ≈ 393.92 km
Rounding to the nearest kilometer, the distance east of A to B is approximately 394 kilometers.
Therefore, point B is approximately 394 kilometers east of point A.