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Architectural Trigonometry
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Flashcards
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Calculating the length of a ramp complying with disability standards
The ramp length is the hypotenuse and is calculated using the sine: length = height / sin(\theta)
Calculating the diagonal length of a rectangular floor to check for squareness during construction
Use the Pythagorean theorem: diagonal = \sqrt{length^2 + width^2}
Determining the length of a bridge’s cable between two towers
The cable length can be approximated using the cosine law for non-right triangles
Adjusting the angle of solar panels for optimal sun exposure
The optimal angle can be found using cos: solar incidence angle = arccos(\frac{sun's elevation}{distance to sun})
Determining the height of a building using its shadow
The height can be found using the inverse tangent to find the angle of elevation: height = shadow length * tan(\theta)
Figuring out the width of a river from a specific point without crossing it
Use trigonometric ratios like tan to calculate the width relying on a reference point opposite to the one standing
Calculating the pitch of a gable roof
Pitch is the tangent of the roof angle to the horizontal: pitch = tan(\theta)
Estimating the amount of material needed for a conical roof
Use the arc length formula with the sine: slant height = radius/sin(\theta)
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