Find the shaded region. Round to the nearest tenth.

That's a circle less what's called a segment, the white part of the circle.

The circle has area A = πr² = π(8.35)²

The circular sector formed by the 100° angle is a fraction of A so has area

S = (100/360) A

The isosceles triangle in the sector has two sides that are radii and an included 100° angle so area

T = (1/2) ab sin θ = (1/2) (8.35)(8.35) sin 100°

The circular segment has area S-T so the area of the pink region is

P = A - (S-T) = A+T-S = π(8.35)² + (1/2) (8.35)² sin 100° - (100/360) π(8.35)²

= (8.35)²(π -(100/360)π + (1/2) sin 100°)

= (8.35)²((260/360)π + (1/2) sin 100°)

I hate ruining a nice exact answer with an approximation, but they asked.

≈ 192.527 square feet

192.5

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.