Imagine that you are standing on the ground 15 feet away from a flagpole. If the top of the flag is 25 feet high, which equation represents the angle θ your feet make with the top of the flag?
tan theta = 25/15
so
theta = tan^-1 (25/15)
To find the equation that represents the angle θ your feet make with the top of the flag, we need to use trigonometry. In this case, we can use the tangent function.
The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. In this scenario, the opposite side is the height of the flag (25 feet), and the adjacent side is the distance from you to the base of the flagpole (15 feet).
Hence, the equation that represents the angle θ can be written as:
tan(θ) = Opposite/Adjacent
tan(θ) = 25/15
Simplifying further:
tan(θ) = 5/3
So, the equation that represents the angle θ your feet make with the top of the flag is:
tan(θ) = 5/3
To find the angle θ that your feet make with the top of the flag, we can use the concept of trigonometry, specifically the tangent function.
First, let's visualize the situation. You are standing on the ground, 15 feet away from a flagpole. The top of the flag is 25 feet high. We can create a right-angled triangle using these measurements.
The vertical side of the triangle represents the height of the flagpole, which is 25 feet. The horizontal side of the triangle represents the distance between you and the flagpole, which is 15 feet. The hypotenuse of the triangle (the side opposite the right angle) is the straight-line distance from your feet to the top of the flagpole.
Now, let's use the tangent function, which relates the opposite side to the adjacent side in a right triangle. In this case, the opposite side is the height of the flagpole, and the adjacent side is the distance between you and the flagpole.
The tangent function is defined as:
tan(θ) = opposite/adjacent
We can rearrange the equation to solve for θ:
θ = tan^(-1)(opposite/adjacent)
Plugging in the values, we get:
θ = tan^(-1)(25/15)
Therefore, the equation representing the angle θ your feet make with the top of the flag is:
θ = tan^(-1)(5/3)