To solve this problem, we need to use the concept of slopes and angles in a right triangle. Here are the steps:

1. Convert the grades into slopes. The slope is simply the grade expressed as a decimal. So, the north slope is 0.10 and the east slope is 0.25.

2. The angle theta we are looking for is the angle between the north and east directions. In a right triangle, the tangent of an angle is equal to the opposite side divided by the adjacent side. Here, the "opposite side" is the difference in the east and north slopes (0.25 - 0.10 = 0.15), and the "adjacent side" is 1 (the horizontal distance).

3. So, we have tan(theta) = 0.15 / 1 = 0.15.

4. To find the angle theta, we need to take the inverse tangent (also known as the arctangent) of 0.15.

5. In most programming languages, you can use the function atan or atan2 to compute the arctangent. Make sure your calculator or programming language is set to give the result in radians.

6. After calculating, you will get theta = atan(0.15) = 0.15 radians.

7. Round to the nearest hundredth as needed. So, theta = 0.15 radians.

Question

To solve this problem, we need to use the concept of slopes and angles in a right triangle. Here are the steps:

1. Convert the grades into slopes. The slope is simply the grade expressed as a decimal. So, the north slope is 0.10 and the east slope is 0.25.

2. The angle theta we are looking for is the angle between the north and east directions. In a right triangle, the tangent of an angle is equal to the opposite side divided by the adjacent side. Here, the "opposite side" is the difference in the east and north slopes (0.25 - 0.10 = 0.15), and the "adjacent side" is 1 (the horizontal distance).

3. So, we have tan(theta) = 0.15 / 1 = 0.15.

4. To find the angle theta, we need to take the inverse tangent (also known as the arctangent) of 0.15.

5. In most programming languages, you can use the function atan or atan2 to compute the arctangent. Make sure your calculator or programming language is set to give the result in radians.

6. After calculating, you will get theta = atan(0.15) = 0.15 radians.

7. Round to the nearest hundredth as needed. So, theta = 0.15 radians.

Knowee AI · Accepted Answer

To solve this problem, we need to use the concept of slopes and angles in a right triangle. Here are the steps:

1. Convert the grades into slopes. The slope is simply the grade expressed as a decimal. So, the north slope is 0.10 and the east slope is 0.25.

2. The angle theta we are looking for is the angle between the north and east directions. In a right triangle, the tangent of an angle is equal to the opposite side divided by the adjacent side. Here, the "opposite side" is the difference in the east and north slopes (0.25 - 0.10 = 0.15), and the "adjacent side" is 1 (the horizontal distance).

3. So, we have tan(theta) = 0.15 / 1 = 0.15.

4. To find the angle theta, we need to take the inverse tangent (also known as the arctangent) of 0.15.

5. In most programming languages, you can use the function atan or atan2 to compute the arctangent. Make sure your calculator or programming language is set to give the result in radians.

6. After calculating, you will get theta = atan(0.15) = 0.15 radians.

7. Round to the nearest hundredth as needed. So, theta = 0.15 radians.

A water main is to be constructed with a 10% grade in the north direction and a 25% grade in the east direction. Determine the angle theta required in the water main for the turn from north to east. provide the answer in radians, round to the nearest hundredth as needed.

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A water main is to be constructed with a 10​% grade in the north direction and a 25​% grade in the east direction. Determine the angle theta required in the water main for the turn from north to east. provide the answer in radians, round to the nearest hundredth as needed.

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A water main is to be constructed with a 10% grade in the north direction and a 25% grade in the east direction. Determine the angle theta required in the water main for the turn from north to east. provide the answer in radians, round to the nearest hundredth as needed.