From the top of a tower, the angles of depression of two objects P and Q (positioned on the ground on the same side of the tower) separated by a distance of (3-√3) m are 45° and 60° respectively. Determine the height of the tower.

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To find the height of the tower, I'll use the angles of depression and the distance between the objects.

**Step 1: Define variables and set up the diagram**  
Let's denote:
- T as the top of the tower
- O as the point directly below T (base of tower)
- H as the height of the tower (TO)
- Let OP = a (distance from tower base to point P)

**Step 2: Use the angle of depression to point Q (60°)**  
The angle of depression to Q is 60°, so:
$$	an 60° = \frac{H}{OQ} = \frac{H}{a}$$

Since $$	an 60° = \sqrt{3}$$:
$$\sqrt{3} = \frac{H}{a}$$
$$	herefore a = \frac{H}{\sqrt{3}}$$

**Step 3: Use the angle of depression to point P (45°)**  
The angle of depression to P is 45°, so:
$$	an 45° = \frac{H}{OP} = \frac{H}{a + (3-\sqrt{3})}$$

Since $$	an 45° = 1$$:
$$1 = \frac{H}{a + (3-\sqrt{3})}$$
$$	herefore a + (3-\sqrt{3}) = H$$

**Step 4: Combine the equations**  
Substituting the value of a from Step 2:
$$\frac{H}{\sqrt{3}} + (3-\sqrt{3}) = H$$

**Step 5: Solve for H**  
$$\frac{H}{\sqrt{3}} + 3 - \sqrt{3} = H$$
$$H + 3\sqrt{3} - 3 = \sqrt{3}H$$
$$3\sqrt{3} - 3 = \sqrt{3}H - H$$
$$3\sqrt{3} - 3 = (\sqrt{3} - 1)H$$
$$(\sqrt{3} - 1)H = 3(\sqrt{3} - 1)$$
$$H = 3$$

Therefore, the height of the tower is **3 meters**.

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