Question - Calculating the Length of a Right-Angled Triangle's Leg
Solution:
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 legSo, 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.
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