1. **Problem 2: Find the missing leg in a right triangle with hypotenuse 15 and one leg 8.** 2. Use the Pythagorean theorem: $$a^2 + b^2 = c^2$$ where $c$ is the hypotenuse. 3. Substitute known values: $$8^2 + b^2 = 15^2$$ 4. Calculate squares: $$64 + b^2 = 225$$ 5. Isolate $b^2$: $$b^2 = 225 - 64$$ 6. Simplify: $$b^2 = 161$$ 7. Take the square root: $$b = \sqrt{161}$$ 8. Approximate: $$b \approx 12.7$$ 1. **Problem 3: Solve for $x$ in a right triangle with legs 72 and 96, hypotenuse $x$.** 2. Use the Pythagorean theorem: $$72^2 + 96^2 = x^2$$ 3. Calculate squares: $$5184 + 9216 = x^2$$ 4. Sum: $$14400 = x^2$$ 5. Take the square root: $$x = \sqrt{14400}$$ 6. Simplify: $$x = 120$$ 1. **Problem 4: Solve for $x$ in a triangle where $x + 38 + 90 = 180$.** 2. Combine known angles: $$x + 128 = 180$$ 3. Isolate $x$: $$x = 180 - 128$$ 4. Simplify: $$x = 52$$ **Final answers:** - Problem 2: $12.7$ - Problem 3: $120$ - Problem 4: $52$