A hot air balloon with a height of 120m is directly over a bridge that is 313m from the balloon's landing point. The navigator finds the angle of depression to the landing point. Find the angle of depression.
as usual, draw a diagram. You will see that
tanθ = 120/313
To find the angle of depression, we can use trigonometry. The angle of depression is the angle between a horizontal line and the line of sight from the observer (in this case, the navigator) to the landing point.
First, let's draw a diagram to visualize the situation.
We have a hot air balloon directly over a bridge, and the navigator is looking down at a certain angle towards the landing point.
Balloon
^
|
| Bridge
|
|------------------------ Landing Point
The vertical distance from the balloon to the landing point is the height of the balloon (120m). The horizontal distance from the balloon to the landing point is given as 313m.
Now, we can use tangent function to calculate the angle of depression. The tangent of an angle is equal to the opposite side divided by the adjacent side.
In this case, the opposite side is the height of the balloon (120m) and the adjacent side is the horizontal distance to the landing point (313m).
So, the tangent of the angle of depression (θ) is:
tan(θ) = opposite / adjacent
tan(θ) = 120 / 313
To find the angle of depression (θ), we need to take the arctangent (inverse tangent) of both sides:
θ = arctan(120 / 313)
Using a calculator or a math tool, we can find the arctangent of 120 divided by 313, which is approximately 20.28 degrees.
Therefore, the angle of depression is approximately 20.28 degrees.