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three towns, a , b, c, are situated ab=300 miles, ac=194 miles, bc=160 miles, b being due north of c. what is the direction from a to b
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Call the sides of the triangle opposite the angles A, B and C; a, b and c respectively. Then use the cosine rule to find angle B from the formula : b² = a²+c²-2.a.c.cosB or 194² = 160²+300²-2×160×300×cosB Having found angle B, the direction from town B to town A is that angle east of south.
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