Angles and the Tangent Ratio

To find an angle on a right angle triangle, we can use the ratio of two sides. If we have the two shorter sides, we calculate the ratio known as the tangent ratio.

To find the angle, label the side opposite the angle we are calculating ‘opp’ for opposite our angle. The other shorter side we label ‘adj’ for ‘adjacent’ or ‘beside’ our angle.

Then we write our formula:

    \[\theta = \tan ^{-1}\frac{\text{opp}}{\text{adj}}\]

Substitute the length of the sides into ‘opp’ and ‘adj’ and use your calculator (on ‘degree’ mode) to find the angle. Find a scientific calculator (realcalc for android works reasonably well if your phone calculator doesn’t have inverse tan), and try our the calculation here:

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