Calculate the included angle:

The fore bearings of line AB and BC are given. Calculate the included angle between them.

(a) FB of AB = 108^o 24′,  FB of BC = 210^o 18′

(b) FB of AB = 16^o 36′,    FB of BC = 323^o 43′

(c) FB of AB = 196^o 37′,  FB of BC = 263^o 19′

Solution

(a) Included angle ABC = ± (FB of BC - BB of AB)

Back bearing of AB = 108^o 24′ + 180^o = 288^o 24′

∠ ABC = 288^o 24′ - 210^o 18′ = 78^o 06′

(b) FB of BC = 323^o 43′

BB of AB = 16^o 36′ + 180^o = 196^o 36′

Included angle ABC = 323^o 43′ - 196^o 36′

= 127^o 07′

(a)

Figure 15 (b)

Figure 15 (c)

(c) FB of AB = 196^o 37′,  FB of BC = 263^o 19′

BB of AB = 196^o 37′ - 180^o

= 16o 37′

Included angle ABC = 263^o 19′ - 16^o 37′ = 246^o 42′ >180^o exterior angle.

Interior angle ABC = 360^o - 246 ^o 42′

= 113^o 18′.