A 20 feet vertical pole cast a shadow of 32 feet. What is the angle of elevation of the sun?
tanx = 20/32 = .625
x = 32°
To find the angle of elevation of the sun, you can use the ratio of the height of the pole to the length of its shadow.
The ratio is given by the tangent of the angle of elevation, which is defined as the opposite side (height of the pole) divided by the adjacent side (length of the shadow).
Tangent = Opposite / Adjacent
In this case, the height of the pole is 20 feet and the length of the shadow is 32 feet.
Tangent (angle) = 20 / 32
To find the angle of elevation, you need to take the inverse tangent (arctangent) of this ratio.
angle = arctan (20 / 32)
Using a calculator or table, you can find the arctan of 20 / 32 to be approximately 33.69 degrees.
So, the angle of elevation of the sun is approximately 33.69 degrees.
To find the angle of elevation of the sun, we can use trigonometry concepts such as the tangent function. Let's assume the angle of elevation of the sun is represented by theta (θ).
The tangent of an angle 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 would be the length of the pole's shadow (32 feet), and the adjacent side would be the height of the pole (20 feet).
Therefore, we can calculate the angle of elevation using the equation:
tan(θ) = opposite/adjacent.
Substituting the values we have:
tan(θ) = 32/20.
To find the angle itself (θ), we can use the inverse tangent (also known as arctan or tan^(-1)).
θ = arctan(32/20).
Now, using a calculator, we can find the angle of elevation of the sun:
θ ≈ 59.04 degrees.
Therefore, the angle of elevation of the sun is approximately 59.04 degrees.