When building a roof, carpenters place posts every 2 feet along the horizontal support beam starting at the eave. Have your students complete the table below in an attempt to discover the relationships between the lengths in the drawing. You may also wish to examine the right triangles in the drawing to further display the relationships.
For the roof, the height of a post depends on its horizontal distance from the eaves. The height increases as the horizontal distance increases, but the ratio of these two quantities remains the same (is constant). The equation h/d = 0.75 can also be written as h = 0.75d. The height of the post "varies directly" with its horizontal distance from the eave. Either equation, stated above, can be used to find the height of a post needed to support the roof. (Example Adapted from Integrated Mathematics 1 by McDougal Littell)
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