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E4004 Surveying Computations A

E4004 Surveying Computations A. Two Missing Distances. Derivation of Formula - Sine Rule. Consider a triangle in which the length of one side is known and the 2 angles at each end of this side are known; i.e. A , C and b are known. C. A. b. Derivation of Formula - Sine Rule.

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E4004 Surveying Computations A

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  1. E4004 Surveying Computations A Two Missing Distances

  2. Derivation of Formula - Sine Rule • Consider a triangle in which the length of one side is known and the 2 angles at each end of this side are known; i.e. A, C and b are known. C A b

  3. Derivation of Formula - Sine Rule • The remaining parts may be calculated by the use of the sine rule B c a C A b

  4. Derivation of Formula - Sine Rule B c a C A b

  5. Derivation of Formula - Traverse • Consider Traverse ABCD • The line AD can be calculated by a close C D B A

  6. Derivation of Formula - Traverse • The triangle ADE has two known angles and one known side and the missing parts can be calculated • Suppose the bearings of two lines DE and EA are known but their distances are unknown C D B A E

  7. Derivation of Formula - Angles • All angles can be calculated by subtracting the known bearings C D B A E

  8. Derivation of Formula - Angles • Earlier discussion suggested that the missing distances could be calculated through an application of the sine rule • Consider finding the sine of angle (EAD) C D B A E

  9. Derivation of Formula - Sine of Angles ……(i) There is a trig identity So but So also So From (i)

  10. Derivation of Formula - Angles C D B A E

  11. Derivation of Formula • Consider triangle ADE C D B A E

  12. Derivation of Formula • Again consider triangle ADE C D B A E

  13. Summary of Two Missing Distance Formula C D B A E

  14. Summary of Two Missing Distance Formula • The two missing distances need not occur consequtively in the traverse • so long as all of the known lines are used to calculate c and c the formula will hold C-D B-C D-E E-F A-B

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