It is known that the center angle of the circle is 40 degrees, the radius is 84.5, and the arc length is 53.059. How to calculate the chord length and chord height? What formula should be used?

It is known that the center angle of the circle is 40 degrees, the radius is 84.5, and the arc length is 53.059. How to calculate the chord length and chord height? What formula should be used?

It is known that in circle 0, angle 0 = 40, AB is chord, 0A = 0b = 84.5. Make 0C vertical AB, intersect AB with D. because A0 = B0, angle a0d = a0b / 2 = 40 / 2 = 20, ab = 2 AD.Rt In triangle a0d, sin20 = ad / 0A, ab = 2ad = 2x0a, sin20 = 2x84.5x0.3420201433 = 57.8014 = 57.8. Similarly, 0d = 84.5cos20 = 79.4, CD = c0-0d = 84.5-79.4 = 5.1

Given the arc length L and chord length m of the sector, how to find the area of the sector,

m^2=r^2+r^2-2r*rcosn
cosn=(2r^2-m^2)/2r^2
l=nπr/180
N and R can be obtained
s=1/2lr=nπr^2/360
One out of two came out

The sector area is 9, the arc length is 6, and the chord length is calculated

Let the radius of the circle where the sector is located be r and the central angle of the circle opposite the sector be n
Then: n / (2 π) * π R & # 178; = 9
n/（2π）*2πR=6 ②
Divide by 2 to get: r = 3
Substituting n = 2
Then: half of the center angle of the circle opposite to the chord length is 2 / 2 = 1
Then half of the chord length is: rsin1 = 3sin1
The chord length is: 3sin1 * 2 = 6sin1

Given that the length of a chord is 12.56, the distance between the middle point of the arc corresponding to the chord and the end point of the chord is 2.5, the sector radius corresponding to the arc is calculated

L=12.56,H=2.5
R=(L^2+4H^2)/(8H)=(12.56^2+4*2.5^2)/(8*2.5)=182.7536/20=9.13768

Circle the arc of a given chord,

Make the vertical bisector of this string. In addition, take another point in the arc and connect it with one end of the string to form a line segment. Then make the vertical bisector of this line segment. The intersection of the two vertical bisectors is the center of the circle
Take the intersection point as the center of the circle and the length from the intersection point to the end of the chord as the radius

It is known that the chord length of an arc is 18cm, and the distance from the center of the circle to the chord is 9cm
According to the vertical diameter theorem, the radius is 9 √ 2, and then l = n π R / 180,?
How to do it? ~ how much is the final? Accurate to. 01cm@@

Radius r = ((18 / 2) ^ 2 + 9 ^ 2) ^ 0.5
=(9^2+9^2)^0.5
=9*(2^0.5)cm
Center angle a = 2 * arc Tan ((18 / 2) / 9)
=2*ARC TAN(1)
=2*45
=90 degrees
=90*PI/180
=5708 radians
Arc length C = ar = 1.5708 * 9 * (2 ^ 0.5)
=19.99cm

How to calculate the area of Arc? (in the case of radius, height and chord length)
When the arc length is unknown

“yangzhihie”：
The arcuate area formula is as follows:
F=0.5[rl-c(r-h)]
Where f is the arcuate area; R is the radius; L is the arc length; C is the chord length; h is the chord height
If we don't know the arc length, we can use the formula: l = 0.01745ra,
Where a is the center angle of the circle
I copied the above formula from the manual of common metal materials. I hope it can help you. Good luck and good bye

The top of the arc is 0.6 meters away from the chord, and the chord length is 3.18 meters. Who can help me calculate the radius of this circle?

2.41

It is known that the chord length is 3.74M, the vertex of the arc is perpendicular to the chord center, and the distance is 0.265m

Given the chord length b = 3.74M and the height h = 0.265m, find the area of the arch. First, find the radius r = (B & # 178; + 4H & # 178;) / 8h = (3.74 & # 178; + 4 × 0.265 & # 178;) / (8 × 0.265) = 14.2689/2.12 = 6.731m, and then find the central angle θ = 4arctan (2H / b) = 4arc (2 × 0.265)

How to calculate arc area with arc length of 5.11m and chord length of 4.8m

Arc length C = 5.11m chord length L = 4.8m how to calculate arc area s? The radius of arc is r, and the center angle of arc is a. RN + 1 = (1 + (L-2 * RN * sin (C / (2 * RN))) / (L-C * cos (C / (2 * RN)))) * rnr0 = 4r1 = 4.175r2 = 4.196r3 = 4.196r = 4.196a = 2 * arc sin ((L / 2) / R) = 2 * arc sin ((4.8 / 2) / 4.1