The length of patio is
.
The left side of roof is
of angle of elevaton.
The rightside angle is
.
Draw the triangle with above specifications :
\
The sum of the angles in any triangle is
.
The length of side is
.
The two angles are
and
.
The remaining angle
.
Law of sines :
.


.
Law of sines : 



The left and right sides of the roof are
and
.
The angle at which the two sides are meet is
.
The left and right sides of the roof are
and
.
The angle at which the two sides are meet is
.