The shadow of the tower standing on a level ground is x m long when the Sun's altitude is 30°, while it is y m long when the altitude is 60°. If the height of the tower is 45√3/2 m, then x−y is

To find the difference between the lengths of the shadows (x - y) when the Sun's altitude is 30° and 60°, we can use trigonometry. The height of the tower is given as \( \frac{45\sqrt{3}}{2} \) meters.

Calculating Shadow Lengths

The length of the shadow can be calculated using the formula:

• Shadow length = Height / tan(Sun's altitude)

For 30° Altitude

Using the altitude of 30°:

• tan(30°) = \( \frac{1}{\sqrt{3}} \)
• Shadow length (x) = \( \frac{45\sqrt{3}/2}{1/\sqrt{3}} = \frac{45\sqrt{3} \cdot \sqrt{3}}{2} = \frac{45 \cdot 3}{2} = \frac{135}{2} \) m

For 60° Altitude

Now, using the altitude of 60°:

• tan(60°) = \( \sqrt{3} \)
• Shadow length (y) = \( \frac{45\sqrt{3}/2}{\sqrt{3}} = \frac{45}{2} \) m

Finding the Difference

Now, we can find the difference between the two shadow lengths:

• x - y = \( \frac{135}{2} - \frac{45}{2} = \frac{135 - 45}{2} = \frac{90}{2} = 45 \) m

The final answer is that x - y equals 45 meters.