Side length 'a' is unknown in each of the above triangles.
This is where Trigonometry comes in. Recall our three basic Trig ratios:
The key to using Trig to solve for an unknown side length is to compare what you know about the triangle to one of those three ratios.
Looking first at the Sine function:
For Cosine:
For Tangent:
Back to our original 3 triangles:
We'll use standard equation solving techniques to isolate the Opposite Side (the unknown in this case).
Therefore, the length of the opposite side is 5.088 units.
Obviously triangles are different and the known values in triangles are different.
Obviously, since there are different types of problems, there is not going to be one single way to solve them.
We have to evaluate three things:
We want to know the length of the Hypotenuse.
We want to find the length of the Hypotenuse. We know the length of the Opposite Side and the Reference Angle.
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