All you need to solve these is a knowledge of the 3 main trigonometrical ratios.
I a right angled triangle where A is a non right angle:-
sin A = opposite / hypotenuse (hypotenuse is the sloping side)
cos A = adjacent / hyptenuse ( the adjacent side is the one the angle 'sits' on)
tan A = opposite / adjacent ( the opposite side is the one opposite the angle)
So to find the length of segment x in the first problem use
sin 61 = x / 50
then
x = 50*sin61 = 43.73
and to find the length of y:-
cos 61 = y / 50
y = 60 cos 61 = 24.24
The other questions can be solved in a similar way.