A plane takes off at an angle of 20 degrees. Assuming a constant speed and trajectory, by the time it has travelled 25 kilometres horizontally, how high will it be flying?
Well, if my calculations are correct, by the time the plane has traveled 25 kilometers horizontally, it will be flying high enough to avoid hitting any trees or buildings. Safety first, you know!
To determine the height the plane is flying, we can use the concept of trigonometry. The angle of takeoff (20 degrees) forms a right triangle with the horizontal distance traveled (25 kilometers) as the base.
We can use the tangent function to find the height of the plane:
tan(angle) = opposite/adjacent
In this case, the height is the opposite side, and the distance traveled is the adjacent side.
tan(20 degrees) = height/25 kilometers
Now we need to solve for the height:
height = 25 kilometers * tan(20 degrees)
Using a calculator, we can calculate the height:
height = 25 kilometers * 0.364
height ≈ 9.1 kilometers
Therefore, the plane will be flying approximately 9.1 kilometers high when it has traveled 25 kilometers horizontally.
To determine how high the plane will be flying after traveling 25 kilometers horizontally, we need to use trigonometry. Specifically, we can use the concept of tangent.
Let's break it down step by step:
Step 1: Identify the given information:
- The angle of takeoff: 20 degrees
- The horizontal distance traveled: 25 kilometers
Step 2: Determine the trigonometric relationship to use:
We are given the angle and the horizontal distance traveled, and we want to find the vertical distance (height). Tangent (tan) relates the ratio of the opposite side to the adjacent side of a right triangle.
Step 3: Set up the appropriate formula:
tan(θ) = opposite/adjacent
Step 4: Substitute the given values:
tan(20 degrees) = opposite/25 kilometers
Step 5: Solve for the opposite side, which represents the height of the plane:
Using a scientific calculator, calculate the tangent of 20 degrees: tan(20) ≈ 0.364
0.364 = opposite/25 kilometers
Step 6: Solve for the opposite side (height):
Multiply both sides of the equation by 25 kilometers:
25 kilometers * 0.364 = opposite
opposite ≈ 9.1 kilometers
Therefore, the plane will be flying approximately 9.1 kilometers high after traveling 25 kilometers horizontally.
A plane takes off at an angle of 20 degrees. Assuming a constant speed and trajectory, by the time it has travelled 25 kilometres horizontally, how high will it be flying?
draw a diagram. You will see that the height
h/25 = tan20°
now just solve for h