What is the length of the radius of a circle with a central angle of 255° that intercepts an arc with length 52 m?
Use π=3.14 in your calculation.
how would i solve this? please help!
arc length = rØ, where r is the radius and Ø is the central angle in radians.
255° = (255/180)π radians = 17π/12
17π/12 r = 52
r = 52(12)/(17π)
= 624/(17π) m
= 11.6838... m using my calculator value of π
or even more simple:
2πr/360 = 52/255
2πr = (52/255)(360)
r = (52/255)(360/2π) = 624/(17π) , same as before
( I always wonder why would a text insist of using π = 3.14 unless it is a very old text? You are probably using a calculator anyway in these calculations, every calculator I have seen lately has a value of π built-in correct to about 10 decimal places)
Well, solving this problem requires a bit of clown wisdom and mathematical skills. So, let's get ready to calculate!
First, we need to find the circumference of the entire circle. To do this, we can use the formula: Circumference = 2πr, where r is the radius.
Since we don't know the radius yet, we'll let it be our x.
Now, we need to find the length of the arc intercepted by the central angle. We can use another formula: Arc Length = (Central Angle / 360°) * Circumference.
Plugging in the given values, we get: 52 m = (255° / 360°) * 2πx
Now, we can do a little math to find x (the radius):
52 m = (255/360) * 2 * 3.14 * x
Simplify: 52 m ≈ 1.4133 * π * x
To solve for x, divide both sides by 1.4133 * π:
52 m ÷ (1.4133 * π) ≈ x
So, my friend, now you can find the approximate value of the radius by evaluating the right side of the equation. Keep in mind that π is approximately 3.14.
But hey, why be exact when you can be approxi-fun?
To solve this problem, you can use the formula for the length of an arc of a circle:
Arc length = (central angle / 360°) * (2 * π * radius)
Given that the central angle is 255° and the arc length is 52m, the formula becomes:
52m = (255° / 360°) * (2 * 3.14 * radius)
Simplifying this equation:
52m = (0.708 * 6.28 * radius)
Now, divide both sides of the equation by (0.708 * 6.28) to solve for the radius:
radius = 52m / (0.708 * 6.28)
Using a calculator, compute the value:
radius ≈ 11.81m
So, the length of the radius of the circle is approximately 11.81 meters.
To solve this problem, we need to use the formula relating the central angle, the radius, and the length of the intercepted arc of a circle. The formula is given by:
Arc length = (Central angle / 360°) * 2π * Radius
Given that the central angle is 255° and the length of the intercepted arc is 52 m, and using π = 3.14, we can rearrange the formula to solve for the radius:
Radius = (Arc length * 360°) / (Central angle * 2π)
Plugging in the values, we have:
Radius = (52 * 360°) / (255 * 2 * 3.14)
Calculating this, we get:
Radius = 18.51 m
Therefore, the length of the radius of the circle is approximately 18.51 meters.