A 12-ft ladder leans against a wall so that the angle between the ground an the ladder is 75 degrees The hight of the ladder reaches up the wall is ( ) feet. Round to one decimal place.

Answer 1

If you draw a right triangle with the height the ladder reaches on the wall as one leg, the ground between the ladder and the wall as the other, and the ladder as the hypotenuse; then the angle opposite the wall measures 75°. We know that the hypotenuse is 12ft. We want the leg opposite our angle measuring 75°. So sin(75°)=x/12ft. Then, multiplying both sides by 12ft, we get that x=12ft⋅sin(75°)≈11.6ft.