Find the length of the intercepted arc, given a central angle of 3pi/5 and a radius of 4.5 cm. Round your answer to the nearest tenth.
Arc length = r * central angle
how to solve(5a)º 7º 8º
To find the length of the intercepted arc, we can use the formula:
Length of intercepted arc = (Central angle / 2π) × (2π × radius)
Given that the central angle is 3π/5 and the radius is 4.5 cm, we can substitute these values into the formula and calculate the length of the intercepted arc.
Length of intercepted arc = (3π/5 / 2π) × (2π × 4.5)
Simplifying this expression, we have:
Length of intercepted arc = (3/5) × (2 × 4.5)
Length of intercepted arc = (3/5) × 9
Length of intercepted arc = 27/5
Now, let's round this value to the nearest tenth. To do this, we look at the digit in the hundredth place, which is 7. Since 7 is greater than or equal to 5, we round up the digit in the tenths place.
Therefore, the length of the intercepted arc, rounded to the nearest tenth, is approximately 5.4 cm.