A 12 ft ladder leaning againist a house make a 64 degree angle with the ground will the ladder reach a window till that is 10.5 ft up from the base of the house?

In triangle ABC

AC = hypotenuse = length of ladder = 12 ft

BC = opposite = height on the wall of house = h

θ = angle of the ladder with the horizontal = 64 deg

using trigonometric formula

Sinθ = opposite/hypotenuse

Sinθ = BC/AC

Sinθ = h/L

Sin64 = h/12

h = 12 Sin64

h = 10.8 ft

since h > 10.5 ft (height of the window)

hence the ladder reach well above the window