Answer: 215.98
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Step-by-step explanation:
Let point C represent the center of the planet.
Segment QC is 2810 miles long as it's one of the radii.
Segment DC is 1970+2810 = 4780 miles long after adding on the height of the mountain.
Triangle DQC is a right triangle. That allows us to use a trig ratio to determine theta. Specifically we'll use cosine.
cos(angle) = adjacent/hypotenuse
cos(theta) = QC/DC
cos(theta) = 2810/4780
theta = arccos(2810/4780)
theta = 53.9942734 degrees approximately
A full 360 degree rotation takes 24 hours. We take a fraction of that to find how many hours it takes for that planet to rotate so point P ends up where point Q is currently located.
(theta/360)*24 = (53.9942734/360)*24 = 3.599618
That's the number of approximate hours it takes. Multiply that by 60 to determine how many minutes it takes.
3.599618*60 = 215.97708
Then that rounds to the final answer 215.98 minutes.