A drone 125 ft high sights a landing pad with an angle of depression of 15 degrees. what is the horizontal distance between the drone and the landing pad?
I tried all the methods set it up multiple ways, and I'm at a loss. My teacher said the answer is 466.5ft.. but how? Thanks so much :-)
very simple, make a sketch.
you will have a right-angled triangle, with a base angle of 15°, the opposite is 125, and let the adjacent be x
tan 15 = 125/x
xtan15 = 125
x = 125/tan15 = 466.506..
Make sure you understand the meaning of "angle of depression". The line of sight would be parallel to the ground, and you have alternate angles of 15°
To find the horizontal distance between the drone and the landing pad, we need to use trigonometry. Specifically, we can use the tangent function to solve this problem.
First, let's define the variables:
h = height of the drone above the ground = 125 ft
θ = angle of depression = 15 degrees
The angle of depression is the angle between the line of sight from the drone to the landing pad and the horizontal plane. Since we are looking for the horizontal distance, we are interested in the adjacent side of the right triangle formed by the drone, the landing pad, and the ground.
Using the tangent function, we have:
tan(θ) = opposite / adjacent
In this case, the opposite side is the height of the drone (h), and the adjacent side is the horizontal distance we want to find (d). So we can rewrite the equation as:
tan(θ) = h / d
Now, substitute the values into the equation:
tan(15 degrees) = 125 ft / d
To solve for d, we need to isolate it. We can rearrange the equation as follows:
d = 125 ft / tan(15 degrees)
Now, calculate the tangent of 15 degrees using a scientific calculator or an online calculator. This will give you the decimal value of the tangent. Let's say it is approximately 0.267949.
Substitute this value into the equation:
d = 125 ft / 0.267949
Now, divide 125 ft by 0.267949 to get the horizontal distance:
d ≈ 466.5 ft
So, the horizontal distance between the drone and the landing pad is approximately 466.5 ft.