After flying at an altitude of 600 meters,a hot air balloon starts to descend when its ground distance from the landing pad is 10 kilomeers.What is the angle of depression for this part of the flight?
tanθ = .6/10
θ = 3.43°
Well, let me put on my "angle of depression" glasses, or as I like to call them, my "downward vision goggles." *Puts on imaginary goggles* Ah, there we go! Now, let's solve this mathematical riddle.
Since the hot air balloon is descending, we need to measure the angle of depression, which is formed by looking downwards from a horizontal line. In this case, from the top of the hot air balloon to the landing pad.
We know that the altitude of the balloon is 600 meters, and the ground distance to the landing pad is 10 kilometers, which is equal to 10,000 meters.
So, we have a right-angled triangle where the altitude is the height, the ground distance is the base, and the angle of depression is our unknown angle.
To find the angle of depression, we can use the tangent function. Tangent is equal to the opposite side (in this case, the altitude) divided by the adjacent side (the ground distance).
Let's calculate it: tangent(angle) = 600 / 10,000
Now, let's put that into a calculator for a quick chuckle...oops, I mean calculation. *Types on calculator* And the answer is approximately 0.06.
Therefore, the angle of depression for this part of the flight is about 0.06 radians or about 3.43 degrees. So, if you were in the hot air balloon, you would be looking down at an angle of approximately 3.43 degrees.
Keep in mind that my calculations are intended for entertainment purposes. Don't rely on a clown's advice for all your mathematical needs!
To find the angle of depression, we can use the tangent function. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the change in altitude (600 meters) and the adjacent side is the ground distance (10 kilometers = 10,000 meters).
So, the angle of depression can be calculated as:
Tangent(angle of depression) = Opposite/Adjacent
Tangent(angle of depression) = 600/10,000
Now, we can solve for the angle of depression.
Angle of depression = arctan(600/10,000)
Using a calculator or trigonometric table, we can find the arctan value:
angle of depression ≈ 3.43 degrees
Therefore, the angle of depression for this part of the flight is approximately 3.43 degrees.
To find the angle of depression, we need to determine the horizontal distance from the balloon to the landing pad and the vertical distance between the balloon and the landing pad.
In this case, the vertical distance is given as 600 meters, and the horizontal distance is given as 10 kilometers (which is equivalent to 10,000 meters).
The angle of depression can be calculated using the following trigonometric formula:
Angle of Depression = arctan(Vertical distance / Horizontal distance)
Substituting the given values:
Angle of Depression = arctan(600 / 10,000)
Now, let's solve it:
Angle of Depression = arctan(0.06)
Using a calculator or trigonometric tables, we can determine that the arctan(0.06) is approximately 3.431 degrees.
Therefore, the angle of depression for this part of the flight is approximately 3.431 degrees.