Write down the given equations and the values of the tangent functions.

We are given two equations:

1. $h = x \tan 60^\circ$
2. $h = (x + 1000) \tan 30^\circ$ We know that $\tan 60^\circ = \sqrt{3}$ and $\tan 30^\circ = \frac{1}{\sqrt{3}}$.

Substitute $\tan 60^\circ = \sqrt{3}$ into equation (1):

$$h = x\sqrt{3} \quad (3)$$

Substitute $\tan 30^\circ = \frac{1}{\sqrt{3}}$ into equation (2):

$$h = (x + 1000)\frac{1}{\sqrt{3}} \quad (4)$$

Set equation (3) equal to equation (4):

$$x\sqrt{3} = (x + 1000)\frac{1}{\sqrt{3}}$$

Multiply both sides by $\sqrt{3}$ to eliminate the fraction:

$$x\sqrt{3} \cdot \sqrt{3} = (x + 1000)\frac{1}{\sqrt{3}} \cdot \sqrt{3}$$ $$3x = x + 1000$$

Subtract $x$ from both sides:

$$3x - x = 1000$$ $$2x = 1000$$

Divide by 2:

$$x = \frac{1000}{2}$$ $$x = 500 \text{ metres}$$

Using $h = x\sqrt{3}$ and $x = 500$:

$$h = 500\sqrt{3}$$

To get a numerical value, use $\sqrt{3} \approx 1.732$:

$$h = 500 \times 1.732$$ $$h = 866 \text{ metres}$$

The values are:
$x = \boxed{\text{500 metres}}$
$h = \boxed{\text{866 metres}}$