Options are:

a:26/3 pi
b:19/12 pi
c:19/6 pi
d:13/3 pi

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

good job you smart son of a gun you are smarter that einstein. 7

the answer is b.

step-by-step explanation:

by the trigonometric ratio tangent, tangent equals opposite divided by adjacent.

therefore, tan(50) equals ac/3

multiply each side by 3 to get: ac=3tan(50)

the answer is b.