Algebra
posted by Ruth .
A 12' ladder leans against a wall at 68 degree angle of elevation. Find the distance from the ladder's base to the wall.

Hi Ruth,this is easy!
Imagine a right angle triangle. In this case, the length of the hypothenuse is 12'.Given the angle of elevation 68 degrees. Since it is a right angle triangle,one of the remaining two angles is 90 degrees. So the third angle is 1809068 = 22 degrees.
Now we know the angles and we know the length of hypothenuse is 12'. We need to find the distance of ladder's base to the wall. Since two angles and a length is known, we have to use sine formula:
a / sin A = b / sin B
Let a = 12' therefore sin A is sin 90 degrees since it is opposite to the hypothenuse. Let b be the distance needed to be found. So sin B is sin 22 degrees since it is opposite to b.
The answer is b = 4.5' 
or, using this equation
x/12 = cos 68° = 0.374
x = 4.46 
The answer is the same anyway :)