Example Question - length calculation
Here are examples of questions we've helped users solve.
Calculating the Length of a Cut in a Metal Workpiece
<p>Leider kann ich keine Lösung anbieten, da das Bild unvollständig ist und wichtige Informationen über die Geometrie des Werkstücks fehlen, was notwendig ist, um die Länge des Brennschnitts zu berechnen.</p>
Calculating the Length of a Right-Angled Triangle's Leg
The image shows a right-angled triangle with the lengths of the hypotenuse and one leg provided. The hypotenuse is 75 cm, and one leg, which is opposite the right angle, is 72 cm. We are asked to find the length of the other leg, which I will call "b." To solve for leg "b," we can use the Pythagorean theorem. 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 legs (a and b). This can be written as: \[ c^2 = a^2 + b^2 \] Where: c = length of the hypotenuse (75 cm) a = length of one leg (72 cm) b = length of the missing leg So, we can rearrange the equation to solve for "b": \[ b^2 = c^2 - a^2 \] Input the known values and solve for "b": \[ b^2 = (75)^2 - (72)^2 \] \[ b^2 = 5625 - 5184 \] \[ b^2 = 441 \] Take the square root of both sides to find the length of "b": \[ b = \sqrt{441} \] \[ b = 21 \] Therefore, the length of the missing leg "b" is 21 cm.
Finding the Missing Side of a Right Triangle
The image shows a right triangle with one side labeled 9, the hypotenuse labeled 18, and the other side labeled x. To find the missing side labeled x, we will use the Pythagorean theorem, which states that for a right-angled triangle \( a^2 + b^2 = c^2 \), where a and b are the lengths of the legs of the triangle, and c is the length of the hypotenuse. Let's solve for x: Given that one leg is 9 and the hypotenuse c, is 18: \[ a^2 + b^2 = c^2 \] \[ 9^2 + x^2 = 18^2 \] \[ 81 + x^2 = 324 \] Now, isolate x^2 by subtracting 81 from both sides: \[ x^2 = 324 - 81 \] \[ x^2 = 243 \] Next, find the square root of both sides to solve for x: \[ x = \sqrt{243} \] \[ x = 15.588 \] (rounded to three decimal places) So, the missing side labeled x is approximately 15.588 units long. However, depending on the context or instructions given, you may need to round this to a different number of decimal places or provide an exact answer in the form of a square root.
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