an air plane takes off with an elevation of 27degrees. what is the total land distance the plane reaches a cruising altitude of 875 feet ? if the plane is traveling at a steady speed of 651 feet per hour, how much time will it take the plane to reach its cruising distance? what would be the angle of elevation if the plane starts descending when it is 400 feet away from the air port landing stri?
h/d = tan 27°
so find d when h=875
if flight distance is f,
d/f = cos 27°
the time needed is thus f/651 hours
tanθ = 875/400
This is just too SIMPLE!!1
To find the total land distance the plane reaches a cruising altitude of 875 feet, we can use trigonometry and the concept of a right-angled triangle. Let's assume that the distance the plane travels along the ground is represented by "x".
In a right-angled triangle, the opposite side is the change in altitude (875 feet) and the angle between the ground and the altitude is 27 degrees. The distance along the ground (x) is the adjacent side.
To find the value of x, we can use the trigonometric function tangent:
tan(27 degrees) = opposite/adjacent
tan(27 degrees) = 875/x
Now, we can solve for x:
x = 875 / tan(27 degrees)
Using a scientific calculator or trigonometric tables, we can find that tan(27 degrees) is approximately 0.5095. Plugging this value into the equation, we have:
x = 875 / 0.5095 ≈ 1715.04 feet
Therefore, the plane reaches a total land distance of approximately 1715.04 feet when it reaches a cruising altitude of 875 feet.
To determine how much time it will take the plane to reach its cruising distance, we can divide the total distance by the plane's speed. Let's assume the speed is 651 feet per hour.
Time = Distance / Speed
Time = 1715.04 feet / 651 feet per hour
Calculating this, we find:
Time ≈ 2.635 hours or approximately 2 hours and 38 minutes
So, it would take the plane about 2 hours and 38 minutes to reach its cruising distance.
To find the angle of elevation when the plane is 400 feet away from the airport landing strip, we can use trigonometry and a similar approach.
In this case, we have a right-angled triangle where the opposite side is the change in altitude (400 feet) and the distance along the ground is the adjacent side. We need to find the angle, which is the angle of elevation.
Using the tangent function again, we can set up the following equation:
tan(angle) = opposite/adjacent
tan(angle) = 400/400
Simplifying the equation, we get:
tan(angle) = 1
To find the angle, we take the arctangent (or inverse tangent) of both sides:
angle = arctan(1)
Using a scientific calculator or trigonometric tables, we find:
angle ≈ 45 degrees
Therefore, the angle of elevation when the plane starts descending and is 400 feet away from the airport landing strip is approximately 45 degrees.