A flagpole 20ft tall cast a shadow 12ft long on the level ground. Find the angle which the rays of the sun make with horizontal
tan (angle) = 20/12
so
angle = tsn^-1 (20/12)
Tan angle 20/12...therefore the angle is tan^-1[20/12)
To find the angle that the sun's rays make with the horizontal, we can use the concept of trigonometry. Specifically, we can use the tangent ratio.
Tangent is defined as the ratio of the length of the opposite side to the length of the adjacent side of a right triangle. In this case, the opposite side is the height of the flagpole (20 ft) and the adjacent side is the length of the shadow (12 ft).
Therefore, we can calculate the tangent of the angle as:
Tan(angle) = Opposite/Adjacent
Tan(angle) = 20/12
To find the actual angle, we need to take the inverse tangent (also known as arctan or tan^-1) of both sides:
Angle = Tan^-1(20/12)
Angle ≈ Tan^-1(1.67)
Using a calculator, we find that the arctan of 1.67 is approximately 59.04 degrees.
So, the angle that the rays of the sun make with the horizontal is approximately 59.04 degrees.
To find the angle which the rays of the sun make with the horizontal, we can use trigonometry. Let's label the height of the flagpole as "h" and the length of its shadow as "s."
Given that the height of the flagpole is 20ft and its shadow is 12ft, we have:
h = 20ft
s = 12ft
Now, let's consider the right triangle formed by the flagpole, its shadow, and the ray of the sun. In this triangle, the side opposite to the angle we want to find is the height of the flagpole (h), and the side adjacent to the angle is the length of the shadow (s).
We can now use the tangent function to find the angle. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side:
tan(angle) = opposite/adjacent
tan(angle) = h/s
Substituting the given values:
tan(angle) = 20ft/12ft
Now, we can find the angle by taking the inverse tangent (arctan) of both sides of the equation:
angle = arctan(20ft/12ft)
Using a calculator or reference table, we can find the arctan value of 20/12 to be approximately 59.04 degrees.
Therefore, the angle that the rays of the sun make with the horizontal is approximately 59.04 degrees.