Calculate the coordinates of C & D

[mwin002]

you have a quadrilateral A,B,C,D See Attached Diagram
you have measure the angles from C & D to A & B

Angle A,D,B = 34°22'10"
Angle B,D,C = 26°54'30"
Angle A,C,B = 17°19'30"
Angle A,C,D = 19°35'00"

Horizontal distance from C to D = 51.05
Point A coordinate = 75.760E, 36.890N
Point B coordinate = 97.897E, 37.010N

Calculate coordinates for C and D and give an independant calculation to check your coordinates.

[Guest]

Just a quick answer while I was thinking about it.........
.....using coordinate geometry and avoiding using anything else...
........and trying to not use some of the surplus info given..........

Let DE,DN be coordinates of point D
Let CE,CN be coordinates of point C

Then (75.76 - DE) / (36.89 - DN) = Tan 26.723 = 0.548

and (97.897 - DE) / (37.01 - DN) = Tan 63.092 = 1.97

1.97 x 37.01 - 1.97xDN = 97.897 - DE

72.9097 - 97.897 - 1.97xDN = -DE

-24.9873 - 1.97DN = -DE

(75.76 - 24.9873 - 1.97DN) / (36.89 - DN) = 0.548

50.773 - 1.97DN = 20.216 -0.548DN

30.557 = 1.422DN

therefore DN = 21.489

and DE = 24.9873 + (1.97 x 21.489) = 67.321

Point D is 67.321E, 21.489N

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For point C, it has same northings...line is horizontal

Point C is (67.321 + 51.05)E, 21.489N

118.371E, 21.489N

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............Simple..............

[Guest]

Aaaaaaaaaaa......maybe the line C to D is not horizontal.......??????
..........in that case my method above is wrong.....at least a bit wrong......????
.........I'll try and do it right the next time.............

[Guest]

.........No I think the line C to D is horizontal, because the diagram shows the line from C to D as 51.05m
......and the Problem states the horizontal distance C to D is 51.05m so line is horizontal.....

So coordinates given in solution above are correct.....except someone proves me wrong....??

...........Simple........

[Guest]

If we know line D to C is horizontal and we know the coordinates of A and also 3 things about the triangle ADC (1 side

and 2 angles) then that is all we need......Point B doesn't matter where it is....???

Angle ADC is 26.908 + 34.369 = 61.277.

So Angle DAC is 180 - 61.277 = 99.14

Using A / Sin A etc....

51.05 / Sin 99.14 = AD / Sin 19.583

So AD = (51.05 x 0.3352 / 0.9873) = 17.332

The vertical (northing) of A relative to D will be AD x Sin 61.277

So vertical coordinate D = 36.89 - (17.332 x 0.877)
= 36.89 - 15.1994
= 21.691
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The horizontal relative to A will be AD x Cos 61.277

So horizontal coordinate D = 75.76 - (17.332 x Cos 61.277)
= 75.76 - (17.332 x 0.4806)
= 75.76 - 8.329
= 67.431
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So coordinates of D are 67.431E, 21.691N

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The coordinates of C will be 51.05 East of A

67.431 + 51.05 = 118.481

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So coordinates of C are 118.481E, 21.691N

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........................Simple....................

[Guest]

Error above

-------------------------
" The coordinates of C will be 51.05 East of A

67.431 + 51.05 = 118.481

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This should read........

The coordinates of C will be 51.05 East of D

67.431 + 51.05 = 118.481

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Calculation is OK

--------------------Simple to make mistakes....................