Example Question - missing leg length
Here are examples of questions we've helped users solve.
Solving for Missing Leg Length of a Right Triangle
The given image shows a right triangle with one leg measuring 13 cm, and the hypotenuse measuring 23 cm. The question likely asks for the length of the other leg of the triangle. We can use the Pythagorean theorem to solve for the missing length. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (the legs). The formula can be written as: \[ c^2 = a^2 + b^2 \] where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the other two sides. Using this theorem and substituting the known values, we get: \[ 23^2 = 13^2 + b^2 \] \[ 529 = 169 + b^2 \] \[ b^2 = 529 - 169 \] \[ b^2 = 360 \] \[ b = \sqrt{360} \] \[ b = 19 \] So the length of the missing leg \( b \) is 19 cm.
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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