Equation for triangle using angles

[ramstin]

What would be the easiest way to find a length of a side of a triangle using its angles, with one length of a side given.

 

[Defennder]

Cosine rule and sine rule.

 

[baba89]

The equation for finding a length of a side of a triangle using its angles is known as the Law of Cosines. This equation states that the square of the length of one side of a triangle is equal to the sum of the squares of the other two sides minus two times the product of those sides and the cosine of the angle opposite the given side.

In other words, if we have a triangle with sides a, b, and c, and angles A, B, and C, and we know the length of one side, say side a, we can use the following equation to find the length of another side, say side b:

b^2 = a^2 + c^2 - 2ac * cos(B)

The easiest way to find the length of a side using this equation would be to first find the value of the cosine of the angle opposite the given side using a scientific calculator. Then, plug in the known values for the other two sides and the angle into the equation and solve for the unknown side.

It's important to note that this equation only works for triangles that are not right triangles. For right triangles, we can use the Pythagorean theorem to find the length of the missing side. Additionally, if we know all three angles of a triangle, we can use the Law of Sines to find the lengths of all three sides.

In conclusion, the Law of Cosines is a useful tool for finding the length of a side of a triangle using its angles, but it is important to consider the type of triangle and use the appropriate equation for the given situation.