Answer:
Explanation:
Let's call the angle of elevation of the sun "θ". We want to find the value of θ.
First, we can find the length of the part of the flagpole that is casting the shadow by using trigonometry. We can define:
h = height of the flagpole above the ground
d = length of the shadow
α = angle of inclination of the flagpole (which is the same as the angle between the ground and the sun's rays, since the flagpole is vertical)
Then, we can use the tangent function to relate these variables:
tan(α) = h/d
Rearranging, we get:
h = d tan(α)
We know that the height of the flagpole is 25 feet, and the length of the shadow is 12 feet. So:
25 = 12 tan(α)
Solving for tan(α), we get:
tan(α) = 25/12
Now we can use the inverse tangent function (also called arctangent) to find α:
α = tan^(-1)(25/12)
α ≈ 65.14 degrees
This is the angle between the ground and the sun's rays, as seen from the flagpole. To find the angle of elevation of the sun, we need to subtract α from 90 degrees (since the sun's rays are perpendicular to the ground). So:
θ = 90 - α
θ ≈ 24.86 degrees
Therefore, the angle of elevation of the sun is approximately 24.86 degrees.