Final answer:
To find the angle of a right triangle without having the measurements of the side, one should employ trigonometric functions such as sine, cosine, and tangent, and their corresponding inverse functions to solve for the unknown angle.
Step-by-step explanation:
To find the angle of a right triangle without the measurement of the side, employ trigonometric functions. Trigonometric functions like sine, cosine, and tangent can relate the angles of a right triangle to the lengths of its sides. For instance, if we know the length of one side and the angle opposite to it, we can use sine (sin), cosine (cos), or tangent (tan) to find the unknown angle. Below is a step-by-step process:
- Identify the known side and angle.
- Select the appropriate trigonometric function based on the available information.
- Use the inverse trigonometric function (such as arcsin, arccos, arctan) to calculate the unknown angle.
Note: The Pythagorean theorem, a² + b² = c², would be helpful only if you have the lengths of the sides and need to find the hypotenuse or another side, not the angle. Moreover, the Law of Sines and Cosines is more commonly used for non-right triangles and when you have more information about the sides and angles. A protractor could be used to directly measure angles, but this is typically less precise than using trigonometric functions, especially for theoretical or algebraic problems.