Find the length of the intercepted arc with radius 2.5 cm and a central angle of 95degrees. Round your answer to the nearest tenth.
Arc length = r * central angle in rads
95 d = 95*pi/180 = 95pi/180 = 19pi/36
19pi/36 = 1.66 rads
Arc length s = 2.5 * 1.66
Arc length s = ?
To find the length of the intercepted arc, we need to use the formula:
Arc Length = (Central Angle / 360) × 2πr
where r is the radius of the circle.
Given: Radius (r) = 2.5 cm
Central Angle = 95 degrees
Using the given values in the formula, we can calculate the length of the intercepted arc.
Arc Length = (95 / 360) × 2π × 2.5
To calculate the length of the intercepted arc, we'll follow these steps:
Step 1: Convert the angle from degrees to radians. Since the formula uses radians, we need to convert degrees to radians by multiplying the angle by (π/180).
Angle in radians = (95 × π) / 180
Step 2: Substitute the values in the formula:
Arc Length = [(95 × π) / 180] × 2π × 2.5
Step 3: Simplify the expression:
Arc Length = (95π × 4π × 2.5) / (180)
Step 4: Calculate the value:
Arc Length ≈ 4.157 cm
Therefore, the length of the intercepted arc, rounded to the nearest tenth, is approximately 4.2 cm.