The sun hits a flagpole that is 180 feet tall. The shadow that is cast is 215 feet. What is the angle of depression?
well, tanθ = 180/215
To find the angle of depression, we need to use trigonometry. The angle of depression is the angle between the horizontal line and the line connecting the top of the flagpole to the point where the shadow touches the ground.
Let's call the angle of depression θ.
We have the opposite side (the height of the flagpole) = 180 feet.
We have the adjacent side (the length of the shadow) = 215 feet.
Using the tangent function, which is the ratio of the opposite side to the adjacent side, we can find the angle of depression.
tan(θ) = opposite/adjacent
tan(θ) = 180/215
To find θ, we take the inverse tangent (arctan) of both sides:
θ = arctan(180/215)
Evaluating this expression using a calculator, we find that the angle of depression is approximately 41.3 degrees.
To find the angle of depression, we need to use trigonometry. The angle of depression is the angle between the line from the sun to the top of the flagpole and the line from the sun to the bottom of the flagpole.
First, let's identify the sides of the triangle. The height of the flagpole is the side opposite the angle of depression, and the shadow length is the side adjacent to the angle of depression.
Using the tangent function, which is the ratio of the opposite side to the adjacent side, we can calculate the angle of depression.
tan(angle of depression) = opposite / adjacent
In this case, the opposite side is the height of the flagpole (180 feet), and the adjacent side is the shadow length (215 feet).
tan(angle of depression) = 180 / 215
Now, we can calculate the angle of depression using the arctan function, also known as the inverse tangent.
angle of depression = arctan(180 / 215)
Using a scientific calculator or online tool, we find that the angle of depression is approximately 40.72 degrees.