Question

In the accompanying figure, the x and y coordinates (in feet) of station A are 1248.16 and 133.35, respectively, and those of station B are 1509.15 and 1101.89, respectively. The length of BP is 2657.45 ft., and the aziμth of line AP is 98.259000. What are the coordinates of station P?

a. X-coordinate of station P

b. Y-coordinate of station P

Answer 1

To calculate the coordinates of station P, we use the azimuth and length of line BP from station B to apply trigonometric calculations and add the results to station A's coordinates.

Step-by-step explanation:

To determine the x-coordinate and y-coordinate of station P, we need to apply trigonometric principles and knowledge of vector magnitudes and directions. Given the azimuth of line AP, we can calculate the delta x and delta y, which when added to the coordinates of station A will give us the coordinates of P. Using the azimuth to find the direction, we have:

• 
  
• Δx = BP × cos(α)
• 
  
• Δy = BP × sin(α)

Considering the azimuth of 98.259000 degrees from the north, converting it first to radians and then applying the trigonometric functions, we find the changes in x and y for the given length of BP, which is 2657.45 ft. Finally, by adding these changes to the coordinates of station A (1248.16, 133.35), we can calculate the coordinates of station P.