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.

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