Question - Solving for Missing Leg Length in a Right-Angled Triangle
Solution:
This image shows a right-angled triangle with one leg of length 75 cm, the hypotenuse of length 72 cm, and the length of the other leg labeled "b."In a right-angled triangle, the Pythagorean theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This can be written as:c² = a² + b²where c is the length of the hypotenuse, and a and b are the lengths of the other two sides. However, from the diagram, we see that they've incorrectly labeled the hypotenuse as shorter than one of the legs, which cannot be the case. So, let's assume that 72 cm is actually the other leg, and "c" represents the hypotenuse of 75 cm. Then we have:c² = a² + b²Solving for b, the equation becomes:b² = c² - a²Substitute the given values:b² = 75² - 72²b² = 5625 - 5184b² = 441Next, find the square root of both sides to solve for b:b = √441b = 21Therefore, the length of the missing leg b is 21 centimeters.
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