Answer:
The length of the shadow of the pole of height 15√3 m at that time is approximately 25.98 m.
Explanation:
We can use trigonometry to solve this problem. Let's assume that the Sun's altitude is represented by the angle θ (in degrees), which is the angle between the horizontal ground and the line from the top of the pole to the Sun.
We know that the tangent of θ is equal to the height of the pole divided by the length of its shadow. So we can write:
tan(θ) = height / shadow length
Substituting the given values, we get:
tan(θ) = 10 / 17.32
Using a calculator, we can find that:
tan(θ) ≈ 0.5774
To find the angle θ, we need to take the arctangent (or inverse tangent) of this value:
θ ≈ 30 degrees
Therefore, the Sun's altitude at that time is 30 degrees.
Now, let's find the length of the shadow of the pole of height 15√3 m at that time. Using the same formula as before, we get:
shadow length = height / tan(θ)
Substituting the known values, we get:
shadow length = (15√3) / tan(30)
Using a calculator, we can simplify this expression and find that:
shadow length ≈ 25.98 m
Therefore, the length of the shadow of the pole of height 15√3 m at that time is approximately 25.98 m.