Solve for height given BMI and weight, and solve for BMI given weight and height.

The Body Mass Index (BMI) is calculated using the formula:

$$BMI = \frac{\text{weight}}{\text{height}^2}$$

To find the height, we rearrange the formula:

$$\text{height}^2 = \frac{\text{weight}}{BMI}$$ $$\text{height} = \sqrt{\frac{\text{weight}}{BMI}}$$

Given:
Weight $= 75 \text{ kg}$
BMI $= 24.2 \text{ kg/m}^2$

$$\text{height} = \sqrt{\frac{75 \text{ kg}}{24.2 \text{ kg/m}^2}}$$

$$\text{height} = \sqrt{3.09917355 \text{ m}^2}$$ $$\text{height} \approx 1.760 \text{ m}$$

The height of the person is approximately $\boxed{\text{1.76 m}}$.

2. Determine the BMI of a person who weighs $75 \text{ kg}$ and is $175 \text{ cm}$ tall.

The BMI formula requires height in meters.

$$175 \text{ cm} = 175 \times \frac{1}{100} \text{ m} = 1.75 \text{ m}$$

$$BMI = \frac{\text{weight}}{\text{height}^2}$$

Given:
Weight $= 75 \text{ kg}$
Height $= 1.75 \text{ m}$

$$BMI = \frac{75 \text{ kg}}{(1.75 \text{ m})^2}$$

$$BMI = \frac{75 \text{ kg}}{3.0625 \text{ m}^2}$$ $$BMI \approx 24.49 \text{ kg/m}^2$$

The BMI of the person is approximately $\boxed{\text{24.49 kg/m}^2\text{}}$.