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.)

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- February 23rd 2006, 06:02 PMcinbadtrig 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.)

- February 24th 2006, 04:07 AMticbolQuote:

Originally Posted by**cinbad**

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.