20 POINTSA circle with a circumference of approximately 15.71 inches drawn inside a square, just touching the sides of the square. Explain how to determine the length of one side of the square.

5.002 inches

step-by-step explanation:

find the diameter of the circlethe diameter is the side length of the square since the sides of it are touching the circle

c = 2πr

c stands for circumferenceπ stands for pi (or 3.14)r stands for radius

- plug in the values given to find the diameter

c = 2πr

15.71 = 2(3.14)r

15.71 = 6.28r

r = 2.501 (rounded or estimated)

now that we have the radius, we can find the diameter by multiplying by 2, since diameter is two times bigger than the radius

diameter = 5.002 (estimated)

now, that will be the side length because the diameter = the side length

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since the cosine is the ratio of the adjacent side to the hypotenuse, you can see that cos 60° = ½. answer. according to the property of cofunctions (topic 3), sin 30° is equal to cos 60°. sin 30° = ½.