The magnitude of a star is a number that is a measure of its brightness
as seen on Earth. The brighter the
star, the lower its magnitude. The
data below show the magnitudes of
five stars in our galaxy. Between
what two integers is the magnitude
of each star located? In most
applications, the magnitude of a
number is its size or amount.
However, when talking about the
magnitude of a star, magnitude
includes negative numbers.

"curse these trig-loving pirates! " devora mutters as she looks at the map. then, after thinking for a moment, she walks back to the entrance of the secret cave, measuring 48 meters along the way. after performing a calculation, devora walks back to the empty treasure, faces the entrance, and turns a certain number of degrees to her left before walking 89 meters to the treasure. supposing that the angle at the cave entrance is acute and that devora's calculations were correct, how many degrees did she turn?