Step-by-step explanation:
the point coordinates at the end of their flights are
x = cos(angle) × distance
y = sin(angle) × distance
remember, cosine is on the x-axis (left and right values), sine is on the y-axis (up and down values).
and the values of sine and cosine are standard for the norm circle with radius = 1.
but in such cases the radius is much larger that 1, and we have to multiply it with the trigonometric functions for scaling reasons.
the radius is always the angled connection from the center of the circle to the point on the arc of the circle. in our cases the travel distances of the shuttles.
so, if we consider the central staffing point as (0, 0), they end up at the following coordinates :
the inner (lower) angle for Mr. Scotts trip is
90-30 = 60°
and his coordinates are
(cos(60)×100, sin(60)×100) =
= (0.5×100, 86.60254038...) = (50, 86.60254038...)
the inner (lower) angle for Mr. Spock's trip is
90-62 = 28°
and his coordinates are
(cos(28)×110, sin(28)×110) =
= (97.12423521..., 51.64187191...)
the distance between these 2 points is
distance² = (Spockx - Scottx)² + (Spocky - Scotty)² =
= (47.12423521...)² + (-34.96066847...)² =
= 2,220.693545... + 1,222.24834... =
= 3,442.941885...
distance = 58.67658719... km
