Question 1085916
If a ladder mounted atop a 10-ft high fire truck
is extended to a length of 48 f, at an angle of {{{45^o}}} ,
it would look like this:
{{{drawing(300,300,-7,45,-4,48,
line(-5,0,45,0),line(0,0,0,50),
rectangle(4,2,43,10),circle(9,1.5,1.5),
circle(36,1.5,1.5),triangle(33,10,35,10,17.87,27.87),
triangle(33,10,35,10,16.13,26.13),
triangle(17.87,27.87,16.13,26.13,0,43),
triangle(17.87,27.87,16.13,26.13,0,45),
red(line(0,10,34,10)),red(line(34,10,0,44)),
red(line(0,10,0,44)),locate(10,7,truck),
red(rectangle(0,10,2,12)),locate(15,0,ground),
locate(-6,20,wall),locate(18,17,ladder)
)}}} Removing the truck {{{drawing(300,300,-7,45,-4,48,
line(-5,0,45,0),line(0,0,0,50),
red(line(0,10,34,10)),red(line(34,10,0,44)),
red(line(0,10,0,44)),
red(rectangle(0,10,2,12)),locate(15,0,ground),
locate(-6,20,wall),locate(18,28,48ft),
locate(0.4,30,x),arc(34,10,16,16,180,225),
locate(27,14,45^o),locate(0.4,6,10ft)
)}}} ,
we just see a right triangle.
It has a {{{90^o}}} angle, of course, and two acute angles.
We are told the bottom acute angle measures {{{45^o}}} ,
so the other acute angle measures {{{90^o-45^o=45^o}}} .
That means it is an isosceles right triangle.
In other words, the distance from the bottom of the ladder to the building wall
is the same as the vertical distance between the bottom of the ladder and the point it touches the building..
The sides of that right triangle measure, x, x, and 48ft.
Applying the Pythagorean theorem, we get
{{{x^2+x^2=(48ft)^2}}}
{{{2x^2=2304ft^2}}}
{{{x^2=1152ft^2}}}
{{{x=sqrt(1152)}}}{{{ft=about33.94ft}}}
So, the top of the ladder is about {{{33.94ft+10fy=43.94ft}}} (or about 44 ft) above ground level.