Arc length and area of a sector question:

Question

3. A radar system has been set up to track approaching weather storms, The radar is set to reach 350 miles and cover an arc of 150 degrees. Find the arc length and the area of the sector that the radar covers.

Answer 1

s = arc length = rθ, where r = radius and θ = radian measure of central angle

 

             s = (350 miles)(5π/6) ≈ 916 miles

 

A = area of sector = (1/2)r²θ = (1/2)(350miles)²(5π/6) ≈ 160,352 mi²

Answer 2

draw the diagram.  problems are easier to solve when you can look at the picture.  you are dealing with part of a circle.