Pregunta
- The legs in a right triangle are 9 inches and 12 inches long. What is the length of
the hypotenuse?
the hypotenuse?
Ask by Ingram Colon. in the United States
Nov 12,2024
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The length of the hypotenuse is 15 inches.
Solución
To find the length of the hypotenuse in a right triangle, you can use the Pythagorean theorem, which states:
where
In this case, the lengths of the legs are 9 inches and 12 inches. Plugging these values into the formula:
Calculating the squares:
Adding these together:
Now, take the square root of both sides to find
Thus, the length of the hypotenuse is 15 inches.
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Simplifique esta solución Beyond the Answer
To find the length of the hypotenuse in a right triangle, you can use the Pythagorean theorem, which states that the square of the hypotenuse © is equal to the sum of the squares of the other two sides (a and b). Here, the legs are 9 inches and 12 inches. So, c² = 9² + 12², which is 81 + 144, equaling 225. Therefore, c = √225, which gives us a hypotenuse of 15 inches. Voila!
This mathematical principle isn’t just for classrooms; it’s widely used in various professions! Architects and engineers rely on the Pythagorean theorem to ensure the structural integrity of buildings, create blueprints, and calculate distances in project designs. The triangle’s properties help them achieve accuracy in their layouts, making this formula a key tool in real-world applications.
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