Answer: 78.69 degrees
Explanation:
We can use trigonometry to find the angle of elevation of the sun. Let's call the angle we're looking for θ. We know that:
tan(θ) = opposite/adjacent
In this case, the opposite side is the height of the mast (50 ft) and the adjacent side is the length of the shadow (10 ft). So we can write:
tan(θ) = 50/10
tan(θ) = 5
To find θ, we need to take the inverse tangent (or arctangent) of both sides:
θ = tan^(-1)(5)
Using a calculator, we find that:
θ ≈ 78.69 degrees
So the angle of elevation of the sun is approximately 78.69 degrees.