the stringer that supports the stairs makes an angle of 50 degrees with the floor. it reaches 3.2 m up the wall. how far is the base of the

For the first one we have

tan(50) = 3.2 / d   where d is the distance from the wall

Rearrange

d = 3.2 / tan (50)  = about 2.69 m

We can use the Pythagorean Theorem for the second

√[3.2^2 + 2.69^2] = about 4.8 m