A homeowner is building a circular fire pit in his backyard. He plans to outline the pit with bricks and cover the space inside
1 answer:
Answer:
<em>1) the exact distance = 9.428571429 feet</em>
<em>the approximate distance = 9.4 feet</em>
<em></em>
<em>2) the exact area = 7.071428571 ft^2</em>
<em>the approximate area = 7 ft^2</em>
<em></em>
Step-by-step explanation:
Required diameter d = 3 feet
1) The distance around the outside of the pit is the circumference of the circle that will be formed by this circular fire pit.
circumference of a circle is given as = πd = x 3 = 9.428571429 feet
the exact distance = 9.428571429 feet
the approximate distance = 9.4 feet
2) The area of the circle that will be formed = =
= 7.071428571 ft^2
the exact area = 7.071428571 ft^2
the approximate area = 7 ft^2
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Cross multiplying gives us
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Divide both sides by 42:
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(61(sin 34))/42 = sin X
Take the inverse sine of both sides:
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Using the Law of Sines, we have:
Cross multiplying gives us
61(sin 34) = 42(sin X)
Divide both sides by 42:
(61(sin 34))/42 = (42(sin X))/42
(61(sin 34))/42 = sin X
Take the inverse sine of both sides:
sin⁻¹((61(sin 34))/42) = sin⁻¹(sin X)
54.3 = X