A 14​-foot ladder is placed against a vertical wall of a​ building, with the bottom of the ladder standing on level ground 6 feet from the base of the building.

Question

I don't understand how you do the problem and how you have to round it to the nearest hundredth.

Answer 1

I will show you two (2) ways to solve this problem.

A diagram is needed to see what is going on....

 

Without loss of generality (WLOG)

The wall is on the right. The ladder leans against the wall

with a POSITIVE slope, from SW to NE (quadrant 3 to quadrant 1).

The measure from the bottom of the ladder to the wall is 6.

 

 

Option 1:

 

 The ladder, ground and wall form a right triangle.

 

 The hypotenuse (ladder) is 14 feet.

 

  The bottom of the ladder is 6 feet from the wall,

   so the base of this right triangle is 6 feet.

 

 The top of the ladder to the ground represents

the missing leg of the right triangle.

 

The pythagorean theorem applies, which says

  6^2 + h^2 = 14^2   where h is the height

                                  of the top of the ladder to the ground

 

36 + h^2 = 196

 

  h^2 = 196 - 36

 

 h^2  = 160

 

 h = sqrt(160)

 

    = sqrt(16 * 10)

 

     = sqrt(16)* sqrt(10)

 

     = 4*sqrt(10) <--- exact answer

 

     = 4 * 3.16227766016838....

 

      = 12.64911....

 

     12.65 <--- rounded to 2 digits as directed

 

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Option #2: using trig

 

With respect to the angle formed by the bottom of the

ladder with the ground

   cos T = 6/14 = 3/7 

  T = inverse-cosine(3/7) = 64.623006647 degrees

 

  sin(64.623006647) = h/14

 

  h = 14*sin(64.62300647) = 12.6491106 <--- same answer

 

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