Find the length of the shadow of a 50 ft vertical pole when the angle of elevation of the sun is 28 degrees
If the shadow has length s,
s/50 = cot 28°
94.03ft
To find the length of the shadow of the vertical pole, we can use trigonometry.
Let's assume the length of the shadow is represented by 'x'.
In this scenario, the vertical pole is the height, and the shadow is the side opposite to the angle of elevation.
The angle of elevation of the sun is 28 degrees, which is the angle between the ground and the line of sight to the top of the pole.
We can use the tangent function (tan) to relate the angle of elevation to the height and shadow length.
The tangent of an angle is equal to the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
In this case, we can set up the following equation:
tan(28 degrees) = height / x
Rearranging the equation to solve for x:
x = height / tan(28 degrees)
Substituting the given height (50 ft) into the equation:
x = 50 ft / tan(28 degrees)
Now we can calculate the length of the shadow by evaluating the tangent of 28 degrees and dividing 50 ft by that value.
Using a calculator, we find:
x ≈ 50 ft / 0.5317
x ≈ 94.03 ft
Therefore, the length of the shadow of the 50 ft vertical pole, when the angle of elevation of the sun is 28 degrees, is approximately 94.03 ft.