36-degree vertical angle. I take that as the angle included by the two slant heights of the roof.Originally Posted bycinbad

Imagine the figure. It is an isosceles triangle whose horizontal base is 14m, and whose apex angle is 36 degrees.

Drop a vertical line segment from the apex to the midpoint of the horizontal base. Two congruent right triangles are formed, each of which has:

---hypotenuse = slant height of roof. Call it side c.

---vertical leg = vertical line segment = unknown.

---horizontal leg = half of 14m = 7m long.

---angle between hypotenuse and vertical leg = half of 36deg = 18deg.

sin(18deg) = 7/c

c*sin(18deg) = 7

c = 7 /sin(18deg)

c = 22.65 meters ----------answer.