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. A C b

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

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

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

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

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

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

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

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

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

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

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

14. 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 A-B B-C C-D D-E E-F