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10 km
My apologies, Mericah! I will switch to English for you. Let's re-do that question.
Guidance for Power Distribution Project (ITEM 1):
Step 1: Calculate the length of the distribution lines. From the given data, we have the position vectors:
The vector for the line from substation A to village B is: The length of the distribution line AB is: The vector for the line from substation A to village C is: The length of the distribution line AC is:
Step 2: Calculate the angle between the distribution lines AB and AC. We use the dot product formula: . The requirement is that the angle between the two distribution lines from the substation must be less than . Since , this condition is met.
Step 3: Determine the appropriate angle of inclination for the distribution line from A to B. The engineer used the equation to represent the inclination of the distribution line from A to B. Case 1: This gives or . Case 2: This gives or . The possible values for are . The distribution line from A to B has vector , which points into the first quadrant (positive slope). Therefore, its angle of inclination should be between and . Among the values found, only is in the first quadrant.
Summary of Guidance:
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My apologies, Mericah! I will switch to English for you. Let's re-do that question.
This languages problem is solved step by step below, with detailed explanations to help you understand the method and arrive at the correct answer.