Answer:
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
Explanation: