Thread: trig is bad

To avoid heavy snow loads on the roof, a ski chalet plan calls for a 36*vertical angle. Assuming the width of the base of the chalet to be 14m, determine the slant height of the roof.(The chalet is in the shape of an isosceles triangle.)

Originally Posted by cinbad

To avoid heavy snow loads on the roof, a ski chalet plan calls for a 36*vertical angle. Assuming the width of the base of the chalet to be 14m, determine the slant height of the roof.(The chalet is in the shape of an isosceles triangle.)

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

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.