I'll do Problem 8 to get you started
a = 4 and c = 7 are the two given sides
Use these values in the pythagorean theorem to find side b
With respect to reference angle A, we have:
- opposite side = a = 4
- adjacent side = b =
- hypotenuse = c = 7
Now let's compute the 6 trig ratios for the angle A.
We'll start with the sine ratio which is opposite over hypotenuse.
Then cosine which is adjacent over hypotenuse
Tangent is the ratio of opposite over adjacent
Rationalizing the denominator may be optional, so I would ask your teacher for clarification.
So far we've taken care of 3 trig functions. The remaining 3 are reciprocals of the ones mentioned so far.
- cosecant, abbreviated as csc, is the reciprocal of sine
- secant, abbreviated as sec, is the reciprocal of cosine
- cotangent, abbreviated as cot, is the reciprocal of tangent
So we'll flip the fraction of each like so:
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Summary:
The missing side is
The 6 trig functions have these results
Rationalizing the denominator may be optional, but I would ask your teacher to be sure.