This geography problem is solved step by step below, with detailed explanations to help you understand the method and arrive at the correct answer.
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Hapa kuna suluhisho la swali lako: Question 1: Horizontal and Vertical Azimuth Angle Computation Easting of Station A (E_A): 315420.550 m Northing of Station A (N_A): 745210.330 m Elevation of Station A (EL_A): 1855.420 m Easting of Station B (E_B): 315685.770 m Northing of Station B (N_B): 745495.610 m Elevation of Station B (EL_B): 1881.960 m Instrument Height (HI): 1.550 m Target Height (HT): 1.800 m a) Compute the departure ( E) and latitude ( N). Step 1: Calculate the departure ( E). Departure is the change in Easting from Station A to Station B. E = E_B - E_A E = 315685.770 m - 315420.550 m E = 265.220 m Step 2: Calculate the latitude ( N). Latitude is the change in Northing from Station A to Station B. N = N_B - N_A N = 745495.610 m - 745210.330 m N = 285.280 m The departure is 265.220 m and the latitude is 285.280 m. b) Determine the horizontal distance between stations A and B. Step 3: Compute the horizontal distance (D). The horizontal distance is calculated using the Pythagorean theorem. D = sqrt(( E)^2 + ( N)^2) D = sqrt((265.220 m))^2 + (285.280 m)^2 D = sqrt(70341.6484 m)^2 + 81384.6784 m^2 D = sqrt(151726.3268 m)^2 D ≈ 389.521 m The horizontal distance is 389.521 m. c) Compute the whole circle horizontal azimuth angle from station A to station B. Step 4: Calculate the whole circle horizontal azimuth angle. Since E is positive and N is positive, the azimuth is in the first quadrant. Azimuth = (( E)/( N)) Azimuth = ((265.220)/(285.280)) Azimuth = (0.92968388) Azimuth ≈ 42.9197^ Convert to degrees, minutes, and seconds: 0.9197^ × 60 = 55.182' 0.182' × 60 = 10.92'' Azimuth = 42^ 55' 11'' The whole circle horizontal azimuth angle is 42^ 55' 11''. d) Compute the vertical angle from station A to station B considering instrument and target heights. Step 5: Calculate the corrected change in elevation ( H). The corrected change in elevation accounts for the instrument height at A and the target height at B. H = (EL_B - EL_A) + (HT - HI) H = (1881.960 m - 1855.420 m) + (1.800 m - 1.550 m) H = 26.540 m + 0.250 m H = 26.790 m Step 6: Compute the vertical angle (_v). The vertical angle is calculated using the corrected change in elevation and the horizontal distance. _v = (( H)/(D)) _v = (26.790 m389.5206 m) _v = (0.068779) _v ≈ 3.9379^ Convert to degrees, minutes, and seconds: 0.9379^ × 60 = 56.274' 0.274' × 60 = 16.44'' _v = 3^ 56' 16'' The vertical angle is 3^ 56' 16''. That's 2 down. 3 left today — send the next one.