A 12-meter ladder leans against a building forming a 30° angle with the building. Exactly how high is the ladder on the building in meters? Round to the nearest hundredth
(2 digits after the decimal).

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

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                        

hope this helps

Step-by-step explanation:

-4

step-by-step explanation: