The string, that supports the stairs, makes an angle of 50° with the floor. it reaches 3.2 m up the wall. how far is the base od the stringer from the wall?

Greetings,

The best way to do these problems is to draw a picture. In this case, you would have a right triangle. I included a picture.

If we use the 54 degree angles as our angle of reference, we are dealing with the opposite side and adjacent side. This makes it a tangent ratio.

We can set up the equation:
tan 54 = 3.2/x
1.19 = 3.2/x    Cross Multiply
1.19x = 3.2     Divide by 1.19
x = 2.69

The base of the stringer is 2.69 m from the wall.

I hope this helps,
MrEQ