How to Find Tangent Ratios
A tangent ratio is a math rule for determining the relationship between the angles and sides of a triangle. This rule allows you to find distance or the length of an entire triangle, or even to determine wave behavior in physics. Most elementary math students are taught the basic principles behind ratios, but it isn't until early high school that you can eventually come to understand how the rule works in its entirety. Know basic division and have a cursory understanding of geometry to find tangent ratios quickly.
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Instructions
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Find Tangent Ratios
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Understand what "ratio" means. A ratio is determined by dividing two quantities. For example, the relationship one-half is a ratio of one to two, which most people commonly understand as "1/2." The slash between the two numbers is a mathematical operator that is the inverse of multiplying.
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Determine the type of triangle you have. There are three basic types of triangles you'll need to consider to find a tangent ratio: acute, right and obtuse. You need to know this in order to find the length of an opposite side later. Remember that all angles in an acute triangle will be less than 90 degrees. A right triangle will have one 90-degree angle, while an obtuse triangle will have one angle that is more than 90 degrees.
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Create an altitude to find the length of the opposite side. The altitude is the height from the apex of a triangle straight down to the base. If you were to imagine a dotted line, the part that intersects with the base will make a right angle. Draw a dotted line, the altitude, opposite of the angle of the tangent that you are trying to find. Measure the length of that altitude and then write it down. Next, measure the distance from the point where the altitude and base meet to one of the angles. Divide the number you first wrote down by the second. This is your tangent ratio.
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Tips & Warnings
Make sure your work is correct by referring to a "trig" table. It is a list of all values for all commonly used math angles.
Keep your measurement units consistent. Avoid varying between inches, feet and yards.
