Tunnel Project Calculations and Concepts

This video tutorial covers the applications of the Law of Cosines, starting with a review of its three forms. It includes a practical example of calculating the length of a tunnel through a mountain and determining the cost and bid amount for the project. Another example involves a transmission tower problem, where the Law of Cosines is used to find the range of service. The video concludes with a discussion on rounding and maintaining consistency in significant digits.

What is the key aspect to remember when using the Law of Cosines?

• The angle used must be the largest angle in the triangle.

• The angle used must be the smallest angle in the triangle.

• The angle used must be opposite the side on the right.

• The angle used must be adjacent to the side on the left.

How is the length of the tunnel calculated using the Law of Cosines?

• By adding the squares of all sides.

• By subtracting the square of one side from the sum of the squares of the other two sides.

• By dividing the sum of the squares of two sides by the cosine of the angle.

• By using the cosine of the angle opposite the side being calculated.

What is the first step in calculating the bid amount for the tunnel project?

• Convert the tunnel length from yards to feet.

• Calculate the total cost in yards.

• Multiply the tunnel length by the cost per yard.

• Determine the profit percentage.

How do you calculate the total cost of drilling the tunnel?

• Subtract the cost per foot from the tunnel length in feet.

• Add the cost per foot to the tunnel length in feet.

• Multiply the tunnel length in yards by the cost per foot.

• Multiply the tunnel length in feet by the cost per foot.

What is the final step in determining the bid amount for the tunnel project?

• Divide the total cost by 1.2.

• Subtract 20% from the total cost.

• Add 20% to the total cost.

• Multiply the total cost by 1.2.

What is the angle formed by the transmission tower's service range?

• 47 degrees

• 31 degrees

• 50 degrees

• 28 degrees

How is the distance where the driver will have service calculated?

• By subtracting the smaller distance from the larger distance.

• By dividing the total distance by the angle.

• By using the Law of Cosines with the given angle and distances.

• By adding the distances to the two sections of I-10.

How long will the driver have service if traveling at 50 miles per hour?

• 29 minutes

• 24 minutes

• 48 minutes

• 50 minutes

Why is it important to round to significant digits in calculations?

• To make the numbers easier to read.

• To maintain consistency with the given data.

• To reduce the number of calculations.

• To ensure all numbers are whole numbers.

What is the reason for maintaining consistency in rounding throughout a problem?

• To avoid using decimals.

• To simplify the calculations.

• To ensure accuracy in the final result.

• To match the textbook's instructions.