Answer:
330.3 degrees
Step-by-step explanation:
sin t = 4√65 / 65 reduces to sin t = 4 / √65. As the sine function is defined as (opp side) / (hypotenuse), we see that opp side = 4 and hyp = √65 must be true. But sin t is positive in Quadrants I and II, not in Quadrant IV.
I will take the liberty of assuming you meant sin t = -4 / √65.
Then (opp side) = -4 and (hyp) = √65.
Use the inverse sine function on a calculator to determine this angle t:
-arcsin(4/√65) comes to -arcsin 0.4961 = -0.5191 radians.
Converting -0.5191 radians to degree measure results in
t = 360° - 29.745°, or 330.2551 degrees. This rounds off to 330.3 degrees.
