How to use the arc length formula

Question

A tower 1,600 yards from an observer subtends an angle of 2 degrees. Use the arc length formula to estimate the height of the tower

Answer 1

The arc length formula is:

s = rθ

where s is the arc length and θ is the angle subtended in radians

since the distance to the tower is 1600 yards and θ is 2º

r = 1600 yds.

θ = 2*(π/180) = π/90 radians

s = 1600(π/90) = 55.85 yds. = 167.55 ft.