Question

Give the degree measure of the arc intercepted by the chord described. Round to the nearest tenth if necessary:

Answer 1

Answer: 60 degrees

Step-by-step explanation:

1. Make a right triangle where the right angle is and label the hypotenuse r.

2. Since the chord is equal to r and a 90-degree angle is formed at the intersection, the chord is bisected. Therefore, the chord segment is 1/2 r.

3. Since we have to solve for the intercepted arc, we must find the central angle ( the angle of the right triangle closest to the dot/center) of the arc, which in this case is the sin, or 0.5r/r.

4. We must get rid of the fraction in the numerator, so multiply both the numerator and denominator by 2 which gets you 1r/2r.

5. The r's cancel out, leaving you with 1/2.

6. Since we have to find the angle measure, you must take the negative sin of 1/2 which is 30 degrees.

7. Finally multiply by 2 since you only solved one bisected portion to get 60 degrees.