This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To calculate the coordinates of points B and C, we use the formulas for coordinate geometry: E_X = E_A + D_AX (_AX) N_X = N_A + D_AX (_AX) where (E_A, N_A) are the coordinates of point A, D_AX is the distance from A to X, and _AX is the azimuth from A to X. Given: Point A coordinates: (E_A, N_A) = (500 m E, 550 m N) a) Calculate coordinates for point B: Distance D_AB = 60 m Azimuth _AB = 30^ 20' 20'' Step 1: Convert the azimuth to decimal degrees. _AB = 30^ + (20)/(60)^ + (20)/(3600)^ = 30^ + 0.333333^ + 0.005556^ = 30.338889^ Step 2: Calculate the Easting coordinate for point B (E_B). E_B = E_A + D_AB (_AB) E_B = 500 m + 60 m × (30.338889^) E_B = 500 m + 60 m × 0.505291 E_B = 500 m + 30.31746 m E_B = 530.317 m Step 3: Calculate the Northing coordinate for point B (N_B). N_B = N_A + D_AB (_AB) N_B = 550 m + 60 m × (30.338889^) N_B = 550 m + 60 m × 0.863005 N_B = 550 m + 51.78030 m N_B = 601.780 m The coordinates of point B are (530.317 m E, 601.780 m N). b) Calculate coordinates for point C: Distance D_AC = 90 m Azimuth _AC = 200^ 33' 55'' Step 1: Convert the azimuth to decimal degrees. _AC = 200^ + (33)/(60)^ + (55)/(3600)^ = 200^ + 0.55^ + 0.015278^ = 200.565278^ Step 2: Calculate the Easting coordinate for point C (E_C). E_C = E_A + D_AC (_AC) E_C = 500 m + 90 m × (200.565278^) E_C = 500 m + 90 m × (-0.351307) E_C = 500 m - 31.61763 m E_C = 468.382 m Step 3: Calculate the Northing coordinate for point C (N_C). N_C = N_A + D_AC (_AC) N_C = 550 m + 90 m × (200.565278^) N_C = 550 m + 90 m × (-0.936216) N_C = 550 m - 84.25944 m N_C = 465.741 m The coordinates of point C are (468.382 m E, 465.741 m N). Send me the next one 📸