A plane takes off at an angle of 24 degrees with the ground. How high in feet is the plane after its flight path is 3 miles long
sin24° = height/3
height = 3sin24
= ...
6442.7 feet?
To find the height of the plane, we can use trigonometry. The angle of 24 degrees is the angle of elevation between the ground and the flight path. By using the tangent function, we can calculate the height.
Let's consider a right triangle with the height (h) as the opposite side and the flight path (3 miles) as the adjacent side. The tangent of the angle (24 degrees) is equal to the ratio of the height to the flight path:
tan(24 degrees) = h / 3 miles
We need to convert miles to feet, as we want the height in feet. Since 1 mile is equal to 5280 feet, the flight path in feet is:
3 miles * 5280 feet/mile = 15,840 feet
Substituting the values into the equation:
tan(24 degrees) = h / 15,840 feet
Rearranging the equation to solve for h:
h = tan(24 degrees) * 15,840 feet
Using a scientific calculator or trigonometric table, we find that tan(24 degrees) is approximately 0.44504187.
Plugging this value into the equation:
h ≈ 0.44504187 * 15,840 feet
h ≈ 7,056.02 feet
Therefore, the plane is approximately 7,056.02 feet high after its flight path of 3 miles.
To find the height of the plane after its flight path, we can use basic trigonometry. Here's how:
Step 1: Convert the angle from degrees to radians.
The angle of 24 degrees needs to be converted to radians for the trigonometric calculation. To convert degrees to radians, multiply the angle by π/180.
In this case, the angle in radians would be (24 * π)/180 = 0.4189 radians (rounded to four decimal places).
Step 2: Use the trigonometric function tangent.
The tangent function is defined as the ratio between the length of the side opposite the angle and the length of the side adjacent to the angle in a right triangle.
In this case, the height of the plane forms the opposite side, and the flight path forms the adjacent side. Therefore, we can use the tangent function to calculate the height.
The tangent of the angle (in radians) is equal to the height of the plane divided by the length of the flight path.
Step 3: Solve for the height.
Let's assume the height of the plane is represented by "h."
So, we have the equation:
tan(angle) = h / flight path
Substituting the known values:
tan(0.4189) = h / 3 miles
Using a calculator to find the tangent of 0.4189, which is approximately 0.4468, we can rewrite the equation as:
0.4468 = h / 3 miles
Now, we can solve for the height by isolating "h" in the equation:
h = 0.4468 * 3 miles
Multiplying 0.4468 by 3 gives us the height in miles.