What is the approximate angle of elevation when a person is 74" tall and the person's shadow is 70" long?
To determine the approximate angle of elevation, we can use trigonometry. The angle of elevation, α, is defined as the angle between the horizontal and the line of sight to the top of the object.
In this case, the height of the person (opposite side) is given as 74 inches, and the length of their shadow (adjacent side) is given as 70 inches.
To find the angle, we can use the tangent function, which is defined as the ratio of the opposite side to the adjacent side:
tan(α) = opposite / adjacent
Substituting the known values:
tan(α) = 74 / 70
To solve for α, we can take the inverse tangent (arctan) of both sides:
α ≈ arctan(74 / 70)
Using a calculator, the approximate value of α is:
α ≈ 45.56 degrees
Therefore, the approximate angle of elevation when a person is 74" tall and their shadow is 70" long is approximately 45.56 degrees.