Question

a circle with circumference 76 has an arc with a 90° angle. what is the length of the arc? show your work here

Explanation:

Step1: Recall the arc - length formula

The formula for the length of an arc \(l\) is \(l=\frac{\theta}{360^{\circ}}\times C\), where \(\theta\) is the central angle of the arc and \(C\) is the circumference of the circle.

Step2: Substitute the given values

We are given that \(C = 76\) and \(\theta=90^{\circ}\). Substituting these into the formula: \(l=\frac{90^{\circ}}{360^{\circ}}\times76\).

Step3: Simplify the fraction

\(\frac{90^{\circ}}{360^{\circ}}=\frac{1}{4}\). So, \(l=\frac{1}{4}\times76\).

Step4: Calculate the result

\(\frac{76}{4}=19\).

Answer:

19