Question

two legs of a right triangle are q and r. the hypotenuse is s. solve for q in terms of the other variables.

Explanation:

Step1: Apply Pythagorean theorem

$q^2 + r^2 = s^2$

Step2: Isolate \( q^2 \)

$q^2 = s^2 - r^2$

Step3: Solve for q (positive root)

$q = \sqrt{s^2 - r^2}$

Answer:

$\sqrt{s^2 - r^2}$