an eight foot ladder leans against a building. if the ladder makes an angle of 60° with the ground, how far up the wall does the ladder reach?

The ladder reaches (4)(√3) ft up the wall (6.93 ft)  

Step-by-step explanation:

Think of a triangle with a 60 degree angle in the lower left corner.  The lower right corner is a right triangle, and 8 ft is the length of the hypotenuse.  The other angle is 30 degrees.

We know the angle 60 degrees, plus the length of the hypotenuse, but need the length of the vertical side opposite the 60 degree angle.  Use the sine function here because it involves these knowns:

                               opposite side

sin 60 degrees = = x/(8 ft) = (√3)/2

Cross-multiplying, we get:

2x = (8 ft)(√3), or through reduction, x = (4)(√3)

The ladder reaches (4)(√3) ft up the wall (6.93 ft)