How to Use Right Triangle Trigonometry as an Architect
- 1). Calculate the angle of a structural element or truss member with a protractor. Find the direction of the loads on the structure; these are either known or calculated from building code requirements given by local municipalities.
Break the direction of the load into horizontal and vertical components. For the horizontal component, multiply the cosine of the member angle by the total load. For the vertical component, multiply the sine of the member angle by the total load.
Double-check your trigonometry by dividing your vertical component by your horizontal component and taking the inverse tangent of your quotient. The angle should be equal to the member angle. - 2). Calculate the angle of the roof or ground slope.
Find the elevation change of a specified horizontal distance by multiplying the tangent of the slope angle by the horizontal distance.
Find the horizontal distance of a given elevation change by dividing the elevation change by the tangent of the slope angle.
Double-check your calculations by taking the inverse tangent of the elevation change divided by the horizontal distance -- if the calculated angle is equal to the slope angle, the calculations are correct. - 3). Calculate the angle of the light coming from the sun or other light source using a protractor.
Find the depth required for an awning or other shading device by dividing the window or aperture height by the tangent of the light angle.
Double-check the angle by finding the inverse tangent of the height divided by the depth. The calculated angle should be equal to the light angle. - 4). Calculate the angle of the light coming from the sun or other light source using a protractor.
Find the height of an object by multiplying the object's shadow length by the tangent of the light angle.
Double-check the angle by finding the inverse tangent of the calculated height divided by the shadow length. If the calculated angle is equal to the light angle, then the height is correct.
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