Example Question - calculate hypotenuse
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Finding the Hypotenuse of a Right Triangle with Given Leg Lengths
<p>The question asks to find the hypotenuse \( c \) of a right triangle with legs \( a = 3 \) and \( b = 4 \).</p> <p>We use the Pythagorean theorem: \( a^2 + b^2 = c^2 \).</p> <p>Substitute the given values: \( 3^2 + 4^2 = c^2 \).</p> <p>Calculate the squares: \( 9 + 16 = c^2 \).</p> <p>Add the results: \( 25 = c^2 \).</p> <p>Take the square root of both sides: \( \sqrt{25} = \sqrt{c^2} \).</p> <p>Thus, \( c = 5 \).</p>
Calculating the Hypotenuse of a Right Triangle
\[ c^2 = a^2 + b^2 \] \[ c^2 = 3^2 + 4^2 \] \[ c^2 = 9 + 16 \] \[ c^2 = 25 \] \[ c = \sqrt{25} \] \[ c = 5 \]
Calculating the Hypotenuse of a Right Triangle
Given \( a = 3 \) and \( b = 4 \) \[ c = \sqrt{a^2 + b^2} \] \[ c = \sqrt{3^2 + 4^2} \] \[ c = \sqrt{9 + 16} \] \[ c = \sqrt{25} \] \[ c = 5 \]
Calculation of Hypotenuse Using Pythagorean Theorem
La imagen muestra tres triángulos, y la instrucción pide calcular el cuadrado de los tres lados de cada triángulo y comprobar que se cumple el Teorema de Pitágoras, que establece que en un triángulo rectángulo, el cuadrado de la hipotenusa (el lado opuesto al ángulo recto) es igual a la suma de los cuadrados de los otros dos lados. Vamos a resolver cada triángulo por separado: 1) Para el primer triángulo: - Lado a = 13 cm - Lado b = 84 cm Aplicamos el Teorema de Pitágoras: \(a^2 + b^2 = c^2\) \(13^2 + 84^2 = c^2\) \(169 + 7056 = c^2\) \(7225 = c^2\) \(c = \sqrt{7225}\) \(c = 85 cm\) 2) Para el segundo triángulo: - Lado a = 50 cm - Lado b = 120 cm Aplicamos el Teorema de Pitágoras: \(a^2 + b^2 = c^2\) \(50^2 + 120^2 = c^2\) \(2500 + 14400 = c^2\) \(16900 = c^2\) \(c = \sqrt{16900}\) \(c = 130 cm\) 3) Para el tercer triángulo: - Lado a = 45 cm - Lado b = 28 cm Aplicamos el Teorema de Pitágoras: \(a^2 + b^2 = c^2\) \(45^2 + 28^2 = c^2\) \(2025 + 784 = c^2\) \(2809 = c^2\) \(c = \sqrt{2809}\) \(c = 53 cm\) De este modo, hemos calculado la hipotenusa de los tres triángulos y verificado que se cumple el Teorema de Pitágoras en cada caso.
Calculating Hypotenuse of a Right Triangle
The image shows a right triangle where the lengths of the two legs are given, which are 60 meters and 80 meters. To find the length of the hypotenuse (c), we can use the Pythagorean theorem: a² + b² = c² Here, 'a' and 'b' are the lengths of the legs of the triangle, and 'c' is the length of the hypotenuse. Plugging the given values into the equation, we get: 60² + 80² = c² 3600 + 6400 = c² 10000 = c² Taking the square root of both sides to solve for 'c' gives us: c = √10000 c = 100 So, the length of the hypotenuse is 100 meters. There's no need to round to the nearest tenth in this case as the result is a whole number.
Finding the Length of the Missing Leg in a Right Triangle
The image shows a right-angled triangle with one of the legs measuring 7 cm and the hypotenuse measuring 25 cm. We are to find the length of the other leg. Since this is a right-angled triangle, we can use the Pythagorean theorem to find the length of the missing side. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): c² = a² + b² Given that the hypotenuse (c) is 25 cm and one of the legs (a) is 7 cm, we can rearrange the equation to solve for the other leg (b): b² = c² - a² b² = 25² - 7² b² = 625 - 49 b² = 576 Taking the square root of both sides gives us the length of b: b = √576 b = 24 cm So, the length of the other leg of the triangle is 24 cm.
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