You have a 20 foot ladder that you are using as you paint your ragetty house. you place the ladder so that it forms an angel of 30 degree with the top of the house. how high will the top of the ladder be above the ground?

In this problem, we are given with the length of 20 ft ladder and the angle of elevation of 30 degrees. Angle of elevation is defined as the angle that is bound between the horizontal and the inclined object, in which in this case is the ladder. The height to the top of the ladder from the roof can be determined using the sin function.

sin Ф = opposite / hypotenuse
The hypotenuse is the length of the ladder in this case.
sin Ф = height / length
sin 30 =  h / 20
0.5 = h/20
h =20*0.5
h = 10 ft

Hence, the height of the ladder from the top of the roof is 10 ft.