A 30-ft. ladder makes an angle of 60 degrees with the horizontal when it reaches a given spot on a wall. What angle will a 35-ft. ladder make the horizontal if it reaches the sample spot?

So first you must find the height at which the "spot" is where the ladder touches the wall ...

sin60=h/30

h=30sin60

Now we can find the angle that the 35 ft ladder make when it touches the same spot.

sinα=h/35 and using h we found earlier ...

sinα = (30sin60) / 35

α=arcsin[ (30sin60) / 35]

α≈47.93 (α≈47º55'42")