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If point A is at (0, 8), point C is at (6, 0), and the distance from p
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09 Dec 2022, 05:59
09 Dec 2022, 05:59
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If point A is at (0, 8), point C is at (6, 0), and the distance from point B to point C is x, what is \(\frac{x}{ \sqrt{7} }\) ?
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Re: If point A is at (0, 8), point C is at (6, 0), and the distance from p
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11 Dec 2022, 04:00
11 Dec 2022, 04:00
Expert Reply
OE
You need to find the length of a leg of a triangle. By finding the lengths of the two other sides, you can use the Pythagorean theorem to find the third side. The hypotenuse of the triangle is the radius of the (quarter-) circle, which, since point A is at (0, 8), is 8. Since point C is (6, 0), the other leg is 6. From the Pythagorean theorem, \(6^2 + x^2 = 8^2\), so \(x^2 = 28\),\( x= \sqrt{28} = \sqrt{4 * 7} = \sqrt{4} * \sqrt{7} = 2 * \sqrt{7}\), so \(\frac{x}{ \sqrt{7} }\)=2 .
You need to find the length of a leg of a triangle. By finding the lengths of the two other sides, you can use the Pythagorean theorem to find the third side. The hypotenuse of the triangle is the radius of the (quarter-) circle, which, since point A is at (0, 8), is 8. Since point C is (6, 0), the other leg is 6. From the Pythagorean theorem, \(6^2 + x^2 = 8^2\), so \(x^2 = 28\),\( x= \sqrt{28} = \sqrt{4 * 7} = \sqrt{4} * \sqrt{7} = 2 * \sqrt{7}\), so \(\frac{x}{ \sqrt{7} }\)=2 .
Re: If point A is at (0, 8), point C is at (6, 0), and the distance from p
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19 Dec 2022, 19:00
19 Dec 2022, 19:00
Carcass wrote:
OE
You need to find the length of a leg of a triangle. By finding the lengths of the two other sides, you can use the Pythagorean theorem to find the third side. The hypotenuse of the triangle is the radius of the (quarter-) circle, which, since point A is at (0, 8), is 8. Since point C is (6, 0), the other leg is 6. From the Pythagorean theorem, \(6^2 + x^2 = 8^2\), so \(x^2 = 28\),\( x= \sqrt{28} = \sqrt{4 * 7} = \sqrt{4} * \sqrt{7} = 2 * \sqrt{7}\), so \(\frac{x}{ \sqrt{7} }\)=2 .
You need to find the length of a leg of a triangle. By finding the lengths of the two other sides, you can use the Pythagorean theorem to find the third side. The hypotenuse of the triangle is the radius of the (quarter-) circle, which, since point A is at (0, 8), is 8. Since point C is (6, 0), the other leg is 6. From the Pythagorean theorem, \(6^2 + x^2 = 8^2\), so \(x^2 = 28\),\( x= \sqrt{28} = \sqrt{4 * 7} = \sqrt{4} * \sqrt{7} = 2 * \sqrt{7}\), so \(\frac{x}{ \sqrt{7} }\)=2 .
What grants us permission to assume the circle is exactly a quarter circle?
