If $15 \, \text{m} = 180 \, \text{feet}$, And The Height Of The Tunnel Is 2700 Meters, Express The Height Of This Tunnel In Feet.

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Understanding the Conversion Factor

To convert the height of the tunnel from meters to feet, we need to establish a conversion factor between meters and feet. The given information states that $15 \, \text{m} = 180 \, \text{feet}$. This means that for every 15 meters, we have 180 feet. We can use this conversion factor to convert the height of the tunnel from meters to feet.

Setting Up the Conversion Factor

The conversion factor can be expressed as a ratio of feet to meters. We can write this as:

$$\frac{180 \, \text{feet}}{15 \, \text{m}}$$

This ratio tells us that for every 15 meters, we have 180 feet.

Converting the Height of the Tunnel

Now that we have the conversion factor, we can use it to convert the height of the tunnel from meters to feet. The height of the tunnel is given as 2700 meters. We can set up a proportion to convert this to feet:

$$\frac{180 \, \text{feet}}{15 \, \text{m}} = \frac{x \, \text{feet}}{2700 \, \text{m}}$$

where $x$ is the height of the tunnel in feet.

Solving for x

To solve for $x$, we can cross-multiply:

$$180 \, \text{feet} \times 2700 \, \text{m} = 15 \, \text{m} \times x \, \text{feet}$$

Simplifying the equation, we get:

$$486000 \, \text{feet} \cdot \text{m} = 15x \, \text{feet}^2$$

Dividing both sides by 15, we get:

$$32400 \, \text{feet} \cdot \text{m} = x \, \text{feet}^2$$

Taking the square root of both sides, we get:

$$x = \sqrt{32400 \, \text{feet} \cdot \text{m}}$$

Simplifying the expression, we get:

$$x = 180 \, \text{feet} \times \sqrt{180}$$

Using a calculator to evaluate the square root, we get:

$$x = 180 \, \text{feet} \times 13.416$$

Multiplying, we get:

$$x = 2414.88 \, \text{feet}$$

Rounding to the nearest whole number, we get:

$$x = 2415 \, \text{feet}$$

Conclusion

In conclusion, the height of the tunnel is approximately 2415 feet.

Additional Information

It's worth noting that the conversion factor can be used to convert any length in meters to feet. For example, if we want to convert 100 meters to feet, we can use the conversion factor:

$$\frac{180 \, \text{feet}}{15 \, \text{m}} = \frac{x \, \text{feet}}{100 \, \text{m}}$$

Solving for $x$, we get:

$$x = \frac{180 \, \text{feet} \times 100 \, \text{m}}{15 \, \text{m}}$$

Simplifying the expression, we get:

$$x = 1200 \, \text{feet}$$

This shows that 100 meters is equivalent to 1200 feet.

Real-World Applications

The conversion factor between meters and feet has many real-world applications. For example, in construction, architects and engineers often need to convert measurements from meters to feet to ensure that buildings and structures are designed and built to the correct specifications. In addition, the conversion factor is also used in navigation and surveying, where it is used to convert distances and heights from meters to feet.

Conclusion

In conclusion, the conversion factor between meters and feet is a useful tool for converting measurements from one unit to another. By using this conversion factor, we can easily convert the height of the tunnel from meters to feet, and we can also use it to convert any length in meters to feet.

Frequently Asked Questions

Q: What is the conversion factor between meters and feet?

A: The conversion factor between meters and feet is 15 meters = 180 feet. This means that for every 15 meters, we have 180 feet.

Q: How do I convert a length in meters to feet using the conversion factor?

A: To convert a length in meters to feet, you can use the following formula:

$$\frac{180 \, \text{feet}}{15 \, \text{m}} = \frac{x \, \text{feet}}{y \, \text{m}}$$

where $x$ is the length in feet and $y$ is the length in meters.

Q: Can I use the conversion factor to convert any length in meters to feet?

A: Yes, you can use the conversion factor to convert any length in meters to feet. Simply plug in the length in meters into the formula and solve for the length in feet.

Q: How do I convert a decimal value in meters to feet using the conversion factor?

A: To convert a decimal value in meters to feet, you can use the following formula:

$$\frac{180 \, \text{feet}}{15 \, \text{m}} = \frac{x \, \text{feet}}{y \, \text{m}}$$

where $x$ is the length in feet and $y$ is the decimal value in meters.

Q: Can I use the conversion factor to convert a length in feet to meters?

A: Yes, you can use the conversion factor to convert a length in feet to meters. Simply plug in the length in feet into the formula and solve for the length in meters.

Q: How do I convert a mixed unit (e.g. 25.5 meters) to feet using the conversion factor?

A: To convert a mixed unit to feet, you can use the following formula:

$$\frac{180 \, \text{feet}}{15 \, \text{m}} = \frac{x \, \text{feet}}{y \, \text{m}}$$

where $x$ is the length in feet and $y$ is the mixed unit in meters.

Q: Can I use the conversion factor to convert a length in meters to other units (e.g. inches, yards)?

A: Yes, you can use the conversion factor to convert a length in meters to other units. However, you will need to use a different conversion factor for each unit.

Q: How do I convert a length in meters to inches using the conversion factor?

A: To convert a length in meters to inches, you can use the following formula:

$$\frac{12 \, \text{inches}}{1 \, \text{foot}} = \frac{x \, \text{inches}}{y \, \text{m}}$$

where $x$ is the length in inches and $y$ is the length in meters.

Q: Can I use the conversion factor to convert a length in meters to yards?

A: Yes, you can use the conversion factor to convert a length in meters to yards. Simply plug in the length in meters into the formula and solve for the length in yards.

Q: How do I convert a length in meters to yards using the conversion factor?

A: To convert a length in meters to yards, you can use the following formula:

$$\frac{3 \, \text{yards}}{1 \, \text{meter}} = \frac{x \, \text{yards}}{y \, \text{m}}$$

where $x$ is the length in yards and $y$ is the length in meters.

Conclusion

In conclusion, the conversion factor between meters and feet is a useful tool for converting measurements from one unit to another. By using this conversion factor, you can easily convert lengths in meters to feet, and you can also use it to convert lengths in feet to meters. Additionally, you can use the conversion factor to convert lengths in meters to other units, such as inches and yards.