Trig Tables and Right Triangles - Mathematics Educators Stack Exchange most recent 30 from matheducators.stackexchange.com 2022-01-27T02:05:32Z https://matheducators.stackexchange.com/feeds/question/12371 https://creativecommons.org/licenses/by-sa/4.0/rdf https://matheducators.stackexchange.com/q/12371 2 Trig Tables and Right Triangles Chaim https://matheducators.stackexchange.com/users/8258 2017-05-25T17:48:09Z 2017-05-27T14:49:25Z <p>I realize that trig tables are somewhat out-of-fashion, but I think my question still makes sense in the computer age: why do trig tables treat the case of a right triangle instead of an arbitrary triangle?</p> <p><a href="https://i.stack.imgur.com/Qt1T7.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/Qt1T7.png" alt="enter image description here"></a></p> <p>Choose a triangle with altitude 1. Label the base angles a and b.</p> <pre><code>Sin a = 1/y Sin b = 1/z Tan a = 1/w Tan b = 1/x </code></pre> <p>Solve each equation for the variable in the denominator:</p> <pre><code>y = 1/Sin a z = 1/Sin b w = 1/Tan a x = 1/Tan b </code></pre> <p>This analysis leads to the creation of a trig table for general triangles. Where two angles are of measure a and b, the three sides will be in the proportion y : z : (w+x). If we divide these three parts by (w+x), the result is a proportion of two parts (usually) not equal to 1, and a third part always equal to 1 and therefore needless to specify.</p> <p><a href="https://i.stack.imgur.com/mEJyy.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/mEJyy.png" alt="enter image description here"></a></p> <p>I think that this statement of the proportion is easier to understand than the usual version. Is the table accurate? Does it make any difference whether we consider an acute, right or obtuse triangle? When have trig tables been done like this before, and why is this version not familiar? If the right triangle format is preferred because it is smaller and fits better on one page, perhaps that preference should be reconsidered in an era in which trig is almost always done on a calculator (or another computer)?</p> https://matheducators.stackexchange.com/questions/12371/-/12378#12378 3 Answer by camelccc for Trig Tables and Right Triangles camelccc https://matheducators.stackexchange.com/users/1615 2017-05-27T14:49:25Z 2017-05-27T14:49:25Z <p>1) Are trig tables out of fashion, no. we just use trig tables that are hard wired into silicon these days.</p> <p>2) the right angle triangle is by far the most important. whenever you split a vector into orthogonal components, for summation, you are using a right angle triangle. Splitting vectors into non-orthogonal components is generally far less useful.</p> <p>3) use the sine or cosine rules for dealing with the few % of cases where someone actually cares about an arbitrary triangle. This was trivial even in the old days when slide rules were still in fashion, let alone with todays computers. </p>