Real World: Architecture & Construction

ACT Math · Axiom Academy

One right triangle hides inside every gable roof — and it fixes the rafter length, the roof angle, and the wall you have to side. Put it in your hands. You're drawing a house that's 24 ft wide with a peaked (gable) roof. The moment you pick how high the ridge sits above the walls, a single right triangle decides three things at once. Raise the ridge and watch the roof's hidden right triangle grow. The sloped rafter is its hypotenuse — so rafter = (run² + rise²) , live. Builders name a roof by its pitch — rise per 12 of run. Set the pitch and read the actual angle the rafter makes with the ceiling: = arctan(rise ÷ 12) . A taller ridge is a bigger triangular gable wall to cover. The gable is a triangle, so area = ½ × base × height = ½ × 24 × rise — drag past the base design and watch the extra siding. One right triangle, three answers: the Pythagorean theorem gives the rafter to cut, the inverse tangent gives the roof angle, and ½ · base · height gives the gable wall to side. The same three moves size a ramp, a staircase stringer, or a truss — anywhere a slope meets a run.

This is the written version of the interactive lesson above. See the full ACT Math course.