# An A-frame Lake House Is 21 Feet Wide. If The Roof Of The Home Makes A 45 Degree Angle With The Base Of The Home, What Is The Length Of The House From Ground Level To The Peak Of The Roof?

45 x 2
/ | .
/   |  .
/__|__.
<--21-->
45      45

Since the angles of a triangle add up to 180 degrees, the angle at the top has to be 90 degrees.  The top angle can also be described as two 45 degree angles to a vertical line bisecting the house to the middle of the floor.  In other words, the two right triangles are mirror images, each with a base of 10.5 feet.  Since the angle at the top of each right triangle is also 45 degrees, the height must also be 10.5 feet.

It's a rather short roof for an A-frame house.  Normally, A frames have about a 60 degree angle at the base.  Are you sure the vertex at the peak isn't 45 degrees, rather than the base angles?

thanked the writer.
Oddman commented
It's a geometry problem, not an architecture problem. It's one more example of the disconnect between school math and real life. 