You cannot find the hypotenuse of a right triangle with only one side. You need at least two pieces of information, such as:
- One side and one angle: Use the trigonometric functions sine, cosine, or tangent to find the hypotenuse.
- Two sides: Use the Pythagorean theorem (a² + b² = c², where c is the hypotenuse) to calculate the hypotenuse.
Example:
Let's say you have a right triangle with one side measuring 5 units and an angle of 30 degrees.
- Identify the known side: The side measuring 5 units is either the opposite or adjacent side depending on the angle.
- Choose the appropriate trigonometric function: Since we know the angle and one side, we can use the trigonometric function that relates the known side and the hypotenuse. In this case, we can use the sine function (sin = opposite/hypotenuse).
- Solve for the hypotenuse: Using the sine function, we get sin(30°) = 5/hypotenuse. Solving for the hypotenuse, we get hypotenuse = 5/sin(30°) = 10 units.
Note: You cannot find the hypotenuse with only one side because there are infinitely many right triangles with that side length.
