Question

in the right triangle abc (right - angled at c), the length of ab is 25 in, the length of ac is 24 in, and the length of bc is a. find the value of a.

Explanation:

Step1: Apply Pythagorean theorem

For right triangle $ABC$, $AB^2 = AC^2 + BC^2$, so $a^2 = AB^2 - AC^2$

Step2: Substitute given values

$a^2 = 25^2 - 24^2 = 625 - 576$

Step3: Calculate and take square root

$a^2 = 49$, so $a = \sqrt{49}$

Answer:

$7$ in