A ladder that is 4.4 m long is leaning against a wall at an angle of 70.0 degrees...

...with respect to the ground. If the base of the ladder is moved 0.51 m away from the wall, how far will the top of the ladder go down?

The ladder forms a rt triangle with the wall
hypotenuse = 4.4
Angle is 70
sin (70) = first height / 4.4
so h1 = 4.4(sin (70))
first base (b1) = 4.4 sin(70)

new base is = b2 = b1+ 0.51
new angle (a2) = inv cos(b2/4.4)
new ht (h2) = 4.4 sin (a2)
delta h = h1-h2

You know a simple way to solve this without even calculate it with trigonometry? You draw it to scale (e.g. 1:100). It might not to accurate, but you will get the round-up number.

This is the hint - try to get the distance of bottom of ladder to wall before and after the ladder is moved. The angle before is 70 degrees, after the ladder is moved, the angle is changed.
You can use inverse sin of the new angle to get the current height of top of ladder to floor. Then find the difference of the height before and after by using cos.
It is simpler if you draw it first.