A person is standing 18 m away from a water tank. The angle of elevation from the person's eye level to the top of the tank is 45 degrees. Calculate the height 'h' of the water tank.

We have a right-angled triangle where:

• The angle of elevation ($\theta$) is $45^\circ$.
• The adjacent side (distance from observer to tower) is $18 \text{ m}$.
• The opposite side (height of the tower, $h$) is unknown.

The tangent function relates the opposite side and the adjacent side to the angle:

$$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$

We know that $\tan(45^\circ) = 1$.

$$1 = \frac{h}{18 \text{ m}}$$

Multiply both sides by $18 \text{ m}$:

$$h = 1 \times 18 \text{ m}$$ $$h = 18 \text{ m}$$