Mathematics, 11.12.2019 12:31, vandonquisenberry

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a segment of a circle has a 120 arc and a chord of 8in. find the area of the segment.

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Our aim is to calculate the Radius so that to use the formula related to the area of a segment of a circle, that is: Aire of segment = Ф.R²/2

Let o be the center of the circle, AB the chord of 8 in subtending the arc f120°

Let OH be the altitude of triangle AOB. We know that a chord perpendicular to a radius bisects the chord in the middle. Hence AH = HB = 4 in

The triangle HOB is a semi equilateral triangle, so OH (facing 30°)=1/2 R. Now Pythagoras: OB² = OH² + 4²==> R² = (R/2)² + 16
R² = R²/4 +16. Solve for R ==> R =8/√3

OB² = OH² +

answered: tammydbrooks43

Step-by-step explanation:

Given that a segment of a circle has a 120 arc and a chord of 8in.

Consider the triangle formed by two radii and the chord of 8 inches. This triangle is isosceles with two sides as equal radii. Hence each base angle is 30 degrees.

By sine formula for triangles

$\frac{r}{sin30} =\frac{8}{sin120} \\r = \frac{8\sqrt{3} }{3}$

Area of segment = area of sector - area of triangle

Area of sector = $\frac{120}{360} (\pi 8^2) = \frac{64\pi}{3}$ ... I

Area of triangle = $\frac{1}{2} r^2 sin 120 =16\sqrt{3}$ ...II

Hence area of segment = I-II = $\frac{64\pi}{3}-16\sqrt{3}$

answered: Guest

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

$4/2 = 2\\7/3.5=2\\8/4=2\\10/5=2$

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

$y=\frac{x}{2}$

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

answered: Guest

dont think so

step-by-step explanation:

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a segment of a circle has a 120 a...