Four Points

[IloveManUtd]

A, B, C and D are four points on horizontal ground with D due east of A. Given that AB = 70m, BC = 80m, CD = 110m and AD = 190 m, and that the angle B is 115[sup:3h7gf2bz]o[/sup:3h7gf2bz], calculate angle ADC and the bearing of B from A

 

[Denis]

Is angleABC = 115 degrees a GIVEN? If so, why is it not stated in problem statement?

 

[mmm4444bot]

Going by the diagram, you could use the Law of Cosines to find AC.

Then, the Law of Sines to find angle BAC.

Back to the Law of Cosines, to find angles ADC and CAD.

They ask for ADC, and the bearing of B from A is CAD + BAC + 90 degrees.

Are you going to start showing some work, on your posts?

 

[BigGlenntheHeavy]

\(\displaystyle After \ all \ is \ said \ and \ done, \ I \ get:\)

\(\displaystyle Angle \ ADC \ \dot= \ 39.675^0 \ and \ bearing \ of \ B \ from \ A \ \dot= \ S21.41^0E.\)

 

[Denis]

\(\displaystyle After \ all \ is \ said \ and \ done, \ .......\)

.....99% has been "said" and 1% (if lucky!) has been done :roll:

 

[mmm4444bot]

I'm thinking that the original poster's source does not use compass designators, when stating bearings. In this case, all bearings are stated as measured clockwise from an initial ray that points due north.

 

[IloveManUtd]

Re:

Going by the diagram, you could use the Law of Cosines to find AC.

Then, the Law of Sines to find angle BAC.

Yeah, I've found length AC = 126.6m, angle BAC = 34.4[sup:10u6v46t]o[/sup:10u6v46t]. I'm having trouble finding the angles of the upper triangle.

 

[Denis]

Re:

I'm thinking that the original poster's source does not use compass designators, when stating bearings. In this case, all bearings are stated as measured clockwise from an initial ray that points due north.

Well, I sure wish he'd start using ANGLES instead of "bearings" :shock:

 

[mmm4444bot]

I've found length AC = 126.6228m, angle BAC = 34.9320[sup:ko21ij7t]o[/sup:ko21ij7t]. I fixed your round-off error, by rounding to four digits.

You get round-off error, when you don't carry enough digits from one calculation to the next. Don't round intermediary results; let your calculator carry all of its digits to the next calculation. Round the final result.

I'm having trouble finding the angles of the upper triangle.

First, find angle ADC. You've got all three sides; use the Law of Cosines.

Then use the Law of Sines to find CAD.

The sum 90-degrees + CAD + CAB is the bearing of B from A.