Use a calculator to determine the unknown angle, to the nearest degree, in each of the following expressions.

tanx=0.75

tany=11 / 5

So:

tan x = 0.75
When putting it into a calculator, you would first have to transpose the equation to make x the subject. So:
x = 0.75
x = 36.87 (to 2 decimal places)

tan y = 
Transpose equation to make y the subject:
y = 
y = 65.56

Just go with the fact that if you want to find the unknown angle, you bring your trigonometric identity (sin, cos or tan, for example) to the other side of the equation, and insert a -1 as a power. Placing a -1 as a power on these ratios makes them inverse ratios, but personally, I don't think it is so important to nut out the reasoning behind this as opposed to getting the process of calculating the unknown angle first.

If you want more info or if my explanation isn't great, I suggest going to https://www.mathsisfun.com/algebra/trig-finding-angle-right-triangle.html as they explain things quite clearly!