A plane has a height of 1000 m. You see the plane at an angle of 40 degrees with the ground . How far away is the plane from where you are standing.
To find the distance between you and the plane, we can use trigonometry.
Let's assume that the distance between you and the plane is represented by 'd'.
In this scenario, we have a right triangle formed by the distance (d), the height of the plane (1000 m), and the angle between the line of sight to the plane and the ground (40 degrees).
In a right triangle, the trigonometric function tangent (tan) can be used to relate the angle and side lengths. Specifically, we can use the tangent function to find d.
The tangent of an angle is equal to the ratio of the opposite side (height of the plane) to the adjacent side (distance between you and the plane).
So, we can write the equation as:
tan(40 degrees) = 1000 m / d
To isolate d, we can rearrange the equation:
d = 1000 m / tan(40 degrees)
Now we can calculate the value of d:
Using a scientific calculator or an online trigonometric calculator, find the tangent of 40 degrees: tan(40 degrees) ≈ 0.8391
Now we substitute this value into the equation:
d = 1000 m / 0.8391
d ≈ 1191.4 m
Therefore, the plane is approximately 1191.4 meters away from your location.