Question - Calculating the Missing Side Length in a Right-Angled Triangle
Solution:
The image shows a right-angled triangle with one of the sides adjacent to the right angle labeled "24 cm" and the hypotenuse labeled "26 cm." To find the length of the other side adjacent to the right angle (often referred to as the opposite side or the height in the context of triangles), we can use the Pythagorean theorem.The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. The theorem is usually 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.Given that $$ c = 26 $$ cm and $$ b = 24 $$ cm, we can solve for $$ a $$:\[ 26^2 = a^2 + 24^2 \]\[ 676 = a^2 + 576 \]\[ a^2 = 676 - 576 \]\[ a^2 = 100 \]\[ a = \sqrt{100} \]\[ a = 10 \]Therefore, the length of the other side adjacent to the right angle (the opposite side) is 10 cm.
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