Question

An arc of length 15ft subtends a central angle 0 in a circle of radios 9ft. Find measure of 0 in degrees

and radians.

Answer 1

The measure of the central angle θ is approximately 95.49° or 5/3 radians, using the arc length formula L = rθ and converting radians to degrees.

Step-by-step explanation:

To find the measure of the central angle θ in degrees and radians, we use the arc length formula:

L = rθ, where L is the arc length, r is the radius of the circle, and θ is the central angle in radians.

Given L = 15 ft and r = 9 ft, we can calculate θ in radians as follows:

θ = L/r = 15/9 = 5/3 radians.

To convert radians to degrees, we use the conversion factor 180°/π:

θ in degrees = (5/3) × (180°/π) ≈ 95.49°.

Therefore, the central angle θ is approximately 95.49° or 5/3 radians.

Answer 2

95.49°

Step-by-step explanation:

The arc length formula is s = rФ, where r is the radius and Ф is the central angle in radians. Here, r = 9 ft and s = 15 ft. Thus, the central angle Ф is

Ф = (15 ft) / (9 ft) = 5/3 radians, or

5 rad 180°

------- * ---------- = 95.49°

3 π rad