Question using the Sine Rule and Bearings

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In summary, three towns located at D, F, and E form the vertices of a scalene triangle. The bearing of F from D is 48 degrees, and the distances between D to E and E to F are 640m and 430m, respectively. Point G is located at the end of a south line at F. Using the equation a/sinA=b/sinB=c/sinC, the angles DFG, GFE, and DFE can be calculated. The angle DFG is 48 degrees, but the angle GFE cannot be determined without more information. The angle DFE can also be calculated. The angle EDF can be calculated using the equation 180-(48+angle DFE).
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scotty_le_b
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Homework Statement


3 towns are located at D,F & E; the vertices of an scalene triangle. The bearing of F from D is 48 degrees. D to E=640m and E to F=430m. Point G is located at the end of a south line at F.

a)i)Find angle DFG
ii) Find angle GFE
iii) Find angle DFE

b) Calculate angle EDF
c)Calculate the bearing of E from D
d)What is the distance between D & F


Homework Equations


a/sinA=b/sinB=c/sinC


The Attempt at a Solution


a)i) I got 48 degrees because I used a z-angle
ii) This is the one I can't get so I can't do the rest. I've tried quite a few ways but can't seem to get it so there must be something I'm missing.
 
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  • #2
I've got it now there was angle missing from the diagram :L
 

1. What is the Sine Rule?

The Sine Rule is a mathematical rule that relates the sides and angles of a triangle. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is equal for all three sides of the triangle.

2. How is the Sine Rule used in finding missing sides?

The Sine Rule can be used to find the length of a missing side in a triangle when the measure of two angles and one side are known. By setting up a proportion using the Sine Rule, the missing side can be solved for using basic algebra.

3. Can the Sine Rule be used with any triangle?

Yes, the Sine Rule can be used with any triangle, regardless of whether it is a right triangle or not. However, it is most commonly used with non-right triangles.

4. How is the Sine Rule used in finding bearings?

The Sine Rule can be used in finding bearings by considering the bearings as angles within a triangle. By setting up a proportion using the Sine Rule and the known bearings, the missing angle in the triangle (which corresponds to the missing bearing) can be solved for.

5. What are some common mistakes when using the Sine Rule?

Common mistakes when using the Sine Rule include forgetting to convert degrees to radians, using the wrong formula for the given scenario (such as using the Cosine Rule instead), and not paying attention to the order of the sides and angles in the proportion.

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