Answer:
The exact length of arc AB is 26/3 π ⇒ a
Step-by-step explanation:
In circle P
∵ A and B lie on the edge of the circle
∴ PA and PB are radii
- All radii of a circle are equal
∴ PA = PB
∵ PB = 15 units
∴ The radius of the circle is 15 units
In Δ APB
∵ PA = PB
∴ m∠A = m∠B
∵ m∠A = 38°
∴ m∠B = 38°
- The sum of the interior angles of a triangles is 180°
∵ m∠A + m∠B + m∠P = 180°
∴ 38° + 38° + m∠P = 180°
∴ 76° + m∠P = 180°
- Subtract 76 from both sides
∴ m∠ P = 104°
The formula of the length of an arc L = (x°/360) × 2πr, where x is the measure of the central angle subtended by this arc
∵ ∠P is a central angle subtended by arc AB
∵ m∠P = 104° and r = 15 units
∴ L = (104/360) × 2π(15)
∴ L = 26/3 π
The exact length of arc AB is 26/3 π
