1. **Problem Statement:** We have two right triangles and need to find the values of $a$ and $b$. 2. **Recall the Pythagorean theorem:** For a right triangle with legs $x$ and $y$, and hypotenuse $c$, the relation is: $$x^2 + y^2 = c^2$$ 3. **Graph 1 (center triangle):** - Base = $a$ - Height = 20 - Hypotenuse = 25 Apply the Pythagorean theorem: $$a^2 + 20^2 = 25^2$$ $$a^2 + 400 = 625$$ Subtract 400 from both sides: $$a^2 = 625 - 400$$ $$a^2 = 225$$ Take the square root: $$a = \sqrt{225} = 15$$ 4. **Graph 2 (bottom-left triangle):** - Height = 175 - Base = $b$ - Hypotenuse = 625 Apply the Pythagorean theorem: $$b^2 + 175^2 = 625^2$$ Calculate squares: $$b^2 + 30625 = 390625$$ Subtract 30625 from both sides: $$b^2 = 390625 - 30625$$ $$b^2 = 360000$$ Take the square root: $$b = \sqrt{360000} = 600$$ **Final answers:** - $a = 15$ - $b = 600$