51. Find the length of the unknown side x of this triangle, evaluate your answer to two decimal places.

Answer:

See work, below.

Step-by-step explanation:

The radius of this circle is 10 and so the diameter is 20.  The measure of the angle opposite side x is found as follows:

                      adj side

 cos theta = ------------------- = 18/20.  Find theta:

                      hypotenuse

theta = arccos 18/20 = 0.451 radian.

Now use the sine function to find x:

                                          x                       x

sin 0.451 radian      = ------------------- = ------------- = 0.651

                                    hypotenuse          20

which results in x = 20(0.651) = 13.02

x = 13.02 units

I should have used the Pythagorean Theorem up front.

18² + x² = 20² becomes x² = 400 - 324 = 76, and so x = √76 ≠ 8.72

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