Cosine Rule Problems - Solve Arbitrarily Chosen Triangles

In summary, the conversation discusses how the law of cosines can be used to solve problems involving triangles, regardless of which sides and angles are chosen. It is noted that the angle must be less than 180 degrees and if it is not, the triangle can still be solved by switching the direction and changing a sign.
  • #1
nDever
76
1
Hey,

If I wanted to make up problems that are solved using the law of cosines, shouldn't it work out even if I arbitrarily choose side a, b, and θ? After all, any two sides and an angle between them form a triangle. Correct?
 
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  • #2
Yes correct. I'm curious to know why you think choosing sides a b and theta wouldn't give you an answer for c.
 
  • #3
You're OK as long as the angle is < 180 deg.
 
  • #4
mathman said:
You're OK as long as the angle is < 180 deg.

Even then you'd just have a triangle in the other direction. You would just have to change a sign(no pun intended).
 
  • #5


Hi there,

Yes, you are correct. The law of cosines can be applied to any triangle, regardless of how the sides and angles are chosen. As long as you have two sides and the included angle, you can use the law of cosines to solve for the remaining side or angle. This is what makes it such a powerful tool in solving triangle problems. So go ahead and create your own problems, as long as they follow the basic rules of a triangle, the law of cosines will work!
 

1. What is the Cosine Rule?

The Cosine Rule is a mathematical formula used to solve triangles that have an arbitrarily chosen angle and two sides.

2. How do I use the Cosine Rule to solve a triangle?

To use the Cosine Rule, you will need to know the measure of one angle and the lengths of two sides of the triangle. Then, plug these values into the formula: c² = a² + b² - 2ab cos(C). Solve for the missing side length.

3. What is an arbitrarily chosen triangle?

An arbitrarily chosen triangle is a triangle where one angle and two sides are known, but not necessarily the angle opposite of one of the given sides.

4. Can the Cosine Rule be used to solve any triangle?

Yes, the Cosine Rule can be used to solve any triangle as long as you know the measure of one angle and the lengths of any two sides.

5. Are there any limitations to using the Cosine Rule?

The Cosine Rule cannot be used when all three angles of a triangle are known. In this case, the Law of Cosines or other trigonometric functions must be used to solve the triangle.

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