1. **State the problem:** Sabrina travels from her house to a park 6.8 miles away. She first goes east 1.6 miles, then north to reach the park. We need to find how far north she travels. 2. **Identify the right triangle:** The path forms a right triangle where: - The eastward leg is 1.6 miles (horizontal leg). - The northward leg is unknown (vertical leg, call it $x$). - The hypotenuse is 6.8 miles (direct distance from house to park). 3. **Use the Pythagorean theorem:** For a right triangle with legs $a$ and $b$ and hypotenuse $c$, the formula is: $$a^2 + b^2 = c^2$$ Here, $a = 1.6$, $b = x$, and $c = 6.8$. 4. **Set up the equation:** $$1.6^2 + x^2 = 6.8^2$$ 5. **Calculate squares:** $$2.56 + x^2 = 46.24$$ 6. **Isolate $x^2$:** $$x^2 = 46.24 - 2.56$$ $$x^2 = 43.68$$ 7. **Find $x$ by taking the square root:** $$x = \sqrt{43.68}$$ 8. **Calculate the square root:** $$x \approx 6.61$$ 9. **Interpret the result:** Sabrina must travel approximately 6.6 miles north to reach the park. **Final answer:** C. 6.6 miles