For large numbers of degrees of freedom, the critical χ2 values can be approximated as follows: χ2 = 12
(z + 2k - 1 )2,
where k is the number of degrees of freedom and z is the critical value. To find the lower critical
value, the negative z-value is used, to find the upper critical value, the positive z-value is used.
Use this approximation to estimate the critical value of χ2 in a right-tailed hypothesis test with
n = 143 and α = 0.01.

"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?