Question - Solving for Missing Leg Length of a Right Triangle
Solution:
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.
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