1. A plane takes off, making an angle of a = 17° with the ground. After the plane travels m = one mile along this flight path, how high (in feet) is it above the ground?. (Round your answer to one decimal place.)
one mile = 5280'
θ=17°
Height = horizontal distance * tan(θ)
=5280' * tan(17°)
Calculate the height.
To solve this problem, we can use trigonometry. Let's break it down step by step:
1. Identify the trigonometric relationship: In this case, we have an angle and a side length opposite to that angle, which suggests the use of the tangent function.
2. Recall the definition of the tangent function: The tangent of an angle is equal to the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. In this case, the side opposite the angle is the height of the plane, and the side adjacent to the angle is the distance the plane traveled along the flight path.
3. Set up the equation: We can write the equation as tan(a) = height / distance, where a represents the angle of 17 degrees, and the distance is given as one mile (which is equal to 5280 feet).
4. Solve for the height: Rearrange the equation to solve for the height: height = distance * tan(a). Plugging in the values, we get height = 5280 feet * tan(17°).
5. Calculate the height: Use a calculator to find the tangent of 17 degrees, and then multiply it by 5280 to get the height of the plane above the ground.
Doing the calculation, we find:
height = 5280 * tan(17°) = 1529.89 feet.
Therefore, the plane is approximately 1530 feet above the ground after traveling one mile along the flight path.