Who knows the area formula of a circle, the arc length formula of a circle, and the sector area formula

Who knows the area formula of a circle, the arc length formula of a circle, and the sector area formula

Area of circle s = π R ² (R is the radius of the circle)
Arc length of circle L=| α|* R （| α| Is the center angle of the circle in radians, and R is the radius of the circle)
Sector area s = 1 / 2 * L * r (L is the arc length of the sector and R is the radius of the circle)
Or = 1 / 2*| α|* R ² （| α| Is the center angle of the circle in radians, and R is the radius of the circle)

Know that the chord length is 10.22 meters, and the highest point from the center of the chord to the arc is 1.37 meters. Calculate the arc length formula, `Please give the length of the arc. Another is to know that the chord length is 10.48m, and the center of the chord to the highest point of the arc is 1.63M Help me with this, too

1. Let the arc radius be r, which is obtained by Pythagorean theorem (10.22 / 2) ²+ (r-1.37) ²= r ² r=10.215sin α= 5.11/10.215=0.5 α= 30 °, then n = 60 ° L = n π R / 180 = 60 × three point one four × 10.215/180 ≈ 10.52. Let the arc radius be r, which is obtained from Pythagorean theorem (10.48 / 2) ²+ (R-1.63)&sup...

Know that the chord length is 8m, and the highest point from the center of the chord to the arc is 1m. Calculate the arc length formula Please give the length of the arc!

Set the circle radius r according to the figure:
R^2=(8/2)^2+(R-1)^2
R = 17 / 2
Find the angle a corresponding to the arc length
sin(a/2)=4/R=28.072
A = 56.145 degrees
Arc length L = 2 * r * 3.14 * 56.145 / 360 = 8.32505
So the arc length is 8.32505 meters

Given the chord length of 30 meters and the area from the chord to the highest point of the arc of 3.65 meters, it is best to write a formula

Given the chord length L = 30m and the highest point of chord to arc H = 3.65m, find the area s?
The arc radius is R and the center angle of the arc is a
R^2=(R-H)^2+(L/2)^2
R^2=R^2-2*R*H+H^2+L^2/4
2*R*H=H^2+L^2/4
R=H/2+L^2/(8*H)
=3.65/2+30^2/(8*3.65)
=32.647m
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((30/2)/32.647)
=54.705 degrees
Sector area s = pi * R ^ 2 * A / 360
=PI*32.647^2*54.705/360
=508.81 M2

Know that the chord length is 5.5, and the center of the chord to the highest point of the arc is 0.5. Calculate the arc length formula

Know that the chord length is 5.5, and the center of the chord to the highest point of the arc is 0.5. Calculate the arc length formula
Given the chord length b = 5.5 and the bow height h = 0.5, the arc radius r = (b) ²+ 4h ²)/ 8h=(5.5 ²+ four × zero point five ²)/ (8 × 0.5)
=(30.25 + 1) / 4 = 7.8125; center angle θ= 4arctan(2h/b)=4arctan(1/5.5)=4 × 0.17985392=0.72
Therefore, the arc length L = R θ= seven point eight one two five × 0.72=5.624

Calculation formula of circle radius corresponding to arc length The 110 meter long straight line makes an arc, and the arc height is 8 meters. It is best to have a calculation formula to calculate the arc length Make an arc with a straight line of 110 meters long and an arc height of 8 meters. Calculate the arc length, the center angle and the radius of the corresponding circle. It is best to have a calculation formula and results

If the center angle corresponding to the arc length is Q and the circle radius is r, then
cos[180Q/(2*3.14)]=(R-8)/R
That is cos [(90 q) / 3.14] = 1-8q / 110
From the above formula, the circle center angle Q and circle radius r = 110 / Q can be obtained