Two Sides and their contained Angle being given to find the third Side and the other Angles.
Two Ships set from one Port, and make an Angle of 58 deg. one sailed N b E, and the other sailed N W 1 deg. 45 min. Westerly, the Eastermost Ship sailed 70 miles and came to her Port: The Westermost Ship sailed 89 miles, and came to her Port: I de∣mand the Distance of these Ports asunder, and how they bear one from the other?
FIrst draw the North and South line A S. Let A B repre∣sent the Port you set from: Then from A as a Center, describe the Arch of 60 deg. F S D: From S to the East∣wards set off one point: for N b E the Eastermost Ships Course draw the line A D at length, and set the first Ships distance 70 miles upon it, which is A B, then from A draw a N W line 4 deg. 45 min. Westerly, and set off the Wester∣most Ships distance run upon that, which is 89 miles, and it reacheth from A to C, draw the line C B from the ends of the other two sides, which is the Distance between the Ports (for the ends of each Ships run must be the Ports) then is A C B the Angle of the bearing of the Eastermost Port from the Westermost, or A B C the bearing of the Westermost Port from the Eastermost, C A is a S E line, 1 deg. 45 min. Easterly from C, see how many points are contained between the C B and C A, by the way that is shewed in the Question before, or because B A is N b E