Question - Finding the Length of a Missing Leg in a Right Triangle
Solution:
The image shows a right triangle with the lengths of two sides provided: one side is 75 cm, and the hypotenuse is 72 cm. The question asks for the length of the missing leg (we will call this b).To find the length of the missing leg, we can use the Pythagorean theorem, which 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). The Pythagorean theorem is written as follows: c^2 = a^2 + b^2In this case, we will rearrange the equation to solve for b:b^2 = c^2 - a^2We know c is 75 cm and a is 72 cm, so let's plug these numbers into the equation:b^2 = 75^2 - 72^2b^2 = 5625 - 5184b^2 = 441Now, to find the length of side b, we take the square root of both sides:b = √441b = 21 cmTherefore, the length of the missing leg b is 21 centimeters.
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