An observer (o) spots a plane flying at a 55 degrees angle to his horizontal line of sight. if the plane is flying at an altitude of 21,000 ft, what is the distance (x) from the plane (p) to the observer (o)?
25,636 ft?
To determine the distance (x) from the plane (p) to the observer (o), we can use trigonometry.
Let's assume that the distance from the plane to the observer forms a right triangle with the altitude of the plane as the height and the distance (x) as the base.
In this case, the angle between the plane and the line of sight is 55 degrees. We can use the tangent function to find the value of x.
The tangent of an angle is defined as the ratio of the opposite side to the adjacent side.
In this scenario, the opposite side is the altitude of the plane (21,000 ft), and the adjacent side is the distance (x) from the plane to the observer.
Using the equation for the tangent of an angle:
tan(55 degrees) = opposite side / adjacent side
tan(55 degrees) = 21,000 ft / x
To find x, we need to rearrange the equation:
x = 21,000 ft / tan(55 degrees)
Calculating the value:
x ≈ 21,000 ft / 1.428
x ≈ 14,671.96 ft
Therefore, the distance from the plane to the observer is approximately 14,671.96 feet.
To find the distance (x) from the plane (p) to the observer (o), we can make use of trigonometry. Specifically, we can use the tangent function, which relates the angle of elevation (in this case, 55 degrees), the opposite side (the altitude of the plane, 21,000 ft), and the adjacent side (the distance from the plane to the observer, x).
The tangent function can be written as:
tan(angle) = opposite / adjacent
In this case, the angle is 55 degrees, the opposite side is 21,000 ft, and the adjacent side is x. We can rearrange the formula to solve for x:
x = opposite / tan(angle)
Substituting the given values:
x = 21,000 ft / tan(55 degrees)
Now, we need to calculate the tangent of 55 degrees. You can use a scientific calculator to find the tangent of 55 degrees, or you can use an online calculator.
Using an online calculator, we find that the tangent of 55 degrees is approximately 1.4281.
Substituting this value back into our equation:
x = 21,000 ft / 1.4281
Simplifying:
x ≈ 14,683 ft
Therefore, the distance from the plane to the observer is approximately 14,683 feet.
sin 55 = 21,000/hypotenuse
we want that hypotenuse