You do not have to use trigonometry to find the answer to these problems. Table 7 of Bowditch tabulates both distance off at the second bearing and predicted distance off when abeam, for a run of one mile between relative bearings from 20° on the bow to 30° on the quarter. Since your distance will rarely equal exactly one mile, the tabulations are in multipliers or factors, which, when multiplied by the actual run give the distance from the object at the time of the second bearing and the predicted distance at which the object should be passed abeam.
Arguments for entering Table 7 are arranged across the top an down the left side of each page. The multipliers or factors are arranged in double columns. The left-hand column lists the factors for finding the distance at the time of the second bearing. The right-hard column contains the factors for finding the predicted distance abeam. Whenever the second bearing is 90° (relative) the two factors are the same. In case the second bearing is greater than 90° (relative), the right hand factor obviously no longer gives a predicted distance abeam, but the estimated distance at which the object was passed abeam.
Distance Off by Bearings (Bowditch Table 7) Distance Abeam
1. Your vessel is steering 263° T at 22 knots. At 0413 a light bears 294° T, and at 0421 the same light bears 312° T. What will be your distance off abeam?
A. 3.4 miles
B. 3.7 miles
C. 4.3 miles
D. 4.9 miles
2. Your vessel is steering 143° T at 16 knots. At 2147 a light bears 106° T, and at 2206 the same light bears 078° T. What will be your distance off abeam?
A. 5.1 miles
B. 5.4 miles
C. 5.9 miles
D. 6.5 miles
3. Your vessel is steering 354° T at 14 knots. At 0317 a light bears 049° T, and at 0342 the same light bears 071° T. What will be your distance off abeam?
A. 12.4 miles
B. 12.7 miles
C. 13.0 miles
D. 13.3 miles
Distance Off by Bearings (Bowditch Table 7) Distance Off at Second Bearing
4. You are steaming on a course of 114° T at 17 knots. At 1122 you observe a lighthouse bearing 077° T. At 1133 the lighthouse bears 051° T. What is your distance off at the second bearing?
A. 3.3 miles
B. 3.9 miles
C. 4.3 miles
D. 4.9 miles
5. You are steaming on a course of 133° T at 16 knots. At 2216 you observe a lighthouse bearing 086° T. At 2223 the lighthouse bears 054° T. What is your distance off at the second bearing?
A. 1.7 miles
B. 2.0 miles
C. 2.3 miles
D. 2.6 miles
6. You are steaming on a course of 327° T at 13 knots. At 0207 you observe a lighthouse bearing 020° T. At 0226 the lighthouse bears 042° T. What is your distance off at the second bearing?
A. 8.5 miles
B. 8.9 miles
C. 9.2 miles
D. 9.7 miles
