How to Determine the Tangent for Right Triangles

The tangent of a triangle can be calculated from lengths of two sides.

Mathematics is a core subject within school and can have important uses in everyday life. Trigonometry, a subset of mathematics, is the study of triangles. The three trigonometric ratios are sine, cosine and tangent. These ratios allow the determination of an angle within a right triangle given the length of two of its sides. Alternatively, if an angle and length of a side are known, the length of the final side can be determined.

Things You'll Need

• Calculator
• Ruler

Instructions

1. Draw the right-angled triangle and label each of the sides and angles. Right-angled triangles have three internal angles, one of which is 90 degrees. The angles within the triangle always add up to 180 degrees. Label the angles and lengths on the triangle. The sides of the triangle are normally labeled as opposite, adjacent and hypotenuse. The adjacent and opposite sides are those emanating from the 90-degree angle. The hypotenuse is the diagonal line opposite the 90-degree angle.

2. Using the ruler to measure each side of the triangle. Annotate the triangle with the measurement values.

3. Calculate the tangent of the right triangle. The tangent of an angle is defined as the opposite / adjacent. For example, if the length of the opposite side is 2 cm and the length of the adjacent side is 1 cm, then the tangent = 2 / 1 = 2.

4. Check the result. The result can be checked by performing an inverse tangent operation. To do this, type the tan ratio found in Step 3 into the calculator and press the "Tan^-1" operation. This is normally done by pressing the "Shift" button, followed by the "Tan" button. The result should yield the value of the original angle.

References

• Clark University: Right Triangles