How to Find Angle Theta in Trigonometry

The measurement of the theta angle can be determined using trigonometric identities.

Trigonometry is the mathematical study of triangles. In trigonometry, the unknown angle measurement in the triangle is called the theta triangle. The measurement of the theta angle can be determined using trigonometric identities.

Things You'll Need

• Scientific or graphic calculator

Instructions

1. Identify angle theta, the unknown angle in the triangle.

2. Identify sides "a," "b" and "c" of the triangle. Side "a" is the side opposite of the theta angle. Side "b" is the side adjacent to the theta angle. Side "c" is the hypotenuse, or the longest side, of the triangle.

3. Select a trigonometric identity to use to find angle theta, depending on the known side lengths. The trigonometric identities are:

   1. sin(theta) = a/c

   2. cos(theta) = b/c

   3. tan(theta) = a/b

4. Plug in the side lengths for the selected trigonometric identity to determine its ratio. For example, if side a = 6 and side c = 10, then sin(theta) = 6/10 or 0.6.

5. Using a scientific or graphic calculator, use the ratio of the identity to determine the measurement of angle theta. On the calculator, select the sin^-1, cos^-1, or tan^-1 key, depending on the trigonometric identity used, then type in the ratio from Step 4. The answer to this function is the measurement of angle theta. For example, if sin(theta) = 0.6, then sin^-1(0.6) = 36.9, and theta angle measures 36.9 degrees.

Tips & Warnings

• Angles can be measured in radians or degrees. Select the appropriate measurement unit on the calculator before beginning.

References

• Shaw Webspace: An Introduction to Trigonometry
• Math2: Trigonometric Identities

Resources

• Read this Article in Spanish