Find the length of a chord intercepted by a central angle of 25 degrees in a circle of radius 30 feet
let the length of the chord be 2x ft
Drop a perpendicular from the central vertex to the chord
then sin 12.5 = x/30
x = 30sin12.5
2x = 60sin12.5 = 12.9864
or by cosine law:
let the length of the chord be c
c^2 = 30^2 + 30^2 - 2(30)(30)cos25
= 168.64598..
c = 12.9864 , same as above
Why did the chord bring a protractor to the circle? Because it wanted to measure its "angle-itude"!
Alright, let's calculate the length of the chord. We know that the length of a chord can be determined using the formula:
Length of Chord = 2 * Radius * sin(θ/2)
Given that the radius is 30 feet and the central angle is 25 degrees, let's plug in the values:
Length of Chord = 2 * 30 * sin(25/2)
Calculating this, we find that the length of the chord intercepted by a 25-degree central angle in a circle with a radius of 30 feet is approximately 20.64 feet.
To find the length of a chord intercepted by a central angle in a circle, you can use the following formula:
Chord Length = 2 * Radius * sin(angle/2)
Given:
Radius (r) = 30 feet
Central angle (θ) = 25 degrees
First, we need to convert the angle from degrees to radians. Since there are π radians in 180 degrees, we can use the following conversion formula:
θ (in radians) = θ (in degrees) * π / 180
θ (in radians) = 25 * π / 180 = 0.4363 radians
Now, we can substitute the values into the formula:
Chord Length = 2 * Radius * sin(θ/2)
Chord Length = 2 * 30 * sin(0.4363/2)
Chord Length ≈ 2 * 30 * sin(0.2181)
Chord Length ≈ 2 * 30 * 0.215
Chord Length ≈ 12.901 feet
Therefore, the length of the chord intercepted by a central angle of 25 degrees in a circle with a radius of 30 feet is approximately 12.901 feet.
To find the length of a chord intercepted by a central angle in a circle, you can use the formula:
Length of chord = 2 * radius * sin(angle/2)
In this case, the radius is 30 feet and the central angle is 25 degrees. Therefore, the formula becomes:
Length of chord = 2 * 30 * sin(25/2)
To calculate this, you first need to convert the angle from degrees to radians, as trigonometric functions usually take angles in radians.
To convert 25 degrees to radians, you can use the following conversion formula:
radians = degrees * pi/180
By substituting the values into the formula, you get:
radians = 25 * pi/180
Now, you can calculate sin(25/2) using a scientific calculator or a math software. Let's assume the value is approximately 0.4226 (rounded to four decimal places).
Substituting the values into the formula:
Length of chord = 2 * 30 * 0.4226
Calculating this expression gives:
Length of chord = 50.76 feet
Therefore, the length of the chord intercepted by a central angle of 25 degrees in a circle with a radius of 30 feet is approximately 50.76 feet.