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. The length of the shadow of a vertical pole 10 m height is 17.32 m at a certain time of a day. What is the Sun's altitude at that time? Also find the length of the shadow of the pole of height 15√3 m at that time.​

User Miatech
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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.

User ErichBSchulz
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