Question

"A telephone line hangs between two poles 14 m apart in the shape of the catenary y = 20cosh(x/20) - 15, where x and y are measured in meters.

(a) Find the slope of this curve where it meets the right pole: The slope is sinh(7/20)

(b) Find the angle θ between the line and the pole: θ = 90° - α, so my question is, why is there an angle α and where is it located?"

Answer 1

The angle theta be described astanθ=sinh(7/20)
θ=tan−1[sinh(7/20)]

its a right triangle...
alpha + theta = 90 theta = 90 - alpha