word problem in geometry

Question

Please help Ido what to dO. A 22 ft ladder reaches a window 18 ft high. How far is the foot of the ladder from the base of the building? How far must the foot of the ladder be moved to the lower the top of the ladder by 2 ft. 

Answer 1

The ladder is the hypotenuse of a right triangle.  The formula for finding the hypotenuse is a²  +  b²  = c²

 

So 18²  + b² = 22²    Now 

 

 

324 + b² = 484  Now subtract 324 from both sides to get the b by itself

b^{2  =  160}

 

find the square root of 160 or 12.649 which is the distance of the foot of the ladder from the base of the building

 

next question.  Lowering the top of the ladder by 2 ft makes it 16 ft high.  Again substitute, same formula

 

16² + b² =  22²

 

256 + b² =484. Now subtract 256 from both sides

          b² =484 -256 or  228.  Now find the sq rt of 228 which is 15.10

Now to get how far the ladder must be moved subtract  like this:  15.10 - 12.649=2.45 feet

 

Note: some teachers allow you to keep answers using the square root and/or exponent form without actually getting a long decimal answer