Finding a Leg of a 5-12-13 Right Triangle
Apply the Pythagorean Theorem and the geometry problem-solving strategy to find an unknown leg of a right triangle when the other leg and the hypotenuse are known.
Problem: Use the Pythagorean Theorem to find the length of the unknown leg of a right triangle with one leg measuring units and a hypotenuse measuring units.
- Read the problem.
- Identify what you are looking for: the length of the leg of the triangle.
- Name: Choose a variable to represent the unknown leg. Let be the length of the leg. Label side on the triangle.
- Translate: Write the Pythagorean Theorem and substitute the known values: then .
- Solve the equation. Evaluate the squares: . Isolate the variable term by subtracting from both sides: . Use the definition of the square root (ignoring the negative root because dimensions correspond to lengths): giving .
- Check the answer. Does ? , which gives .
- Answer: The length of the leg is units.
Unlike finding a hypotenuse — where the two known leg squares are simply summed — finding a missing leg requires subtracting the square of the known leg from the square of the hypotenuse before taking the square root.
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