Tree Height 237E03

1. **State the problem:** A bird is initially 4 meters from the base of an oak tree and flies 5 meters to reach the top of the tree. We need to find the height of the tree. 2. **Identify the formula and concept:** This is a right triangle problem where the bird's initial position, the height of the tree, and the distance the bird flew form a right triangle. Using the Pythagorean theorem: $$a^2 + b^2 = c^2$$ where: - $a$ is the height of the tree (unknown), - $b$ is the horizontal distance from the base (4 meters), - $c$ is the hypotenuse, the distance the bird flew (5 meters). 3. **Set up the equation:** $$a^2 + 4^2 = 5^2$$ 4. **Calculate:** $$a^2 + 16 = 25$$ 5. **Isolate $a^2$:** $$a^2 = 25 - 16$$ $$a^2 = 9$$ 6. **Find $a$ by taking the square root:** $$a = \sqrt{9}$$ $$a = 3$$ 7. **Conclusion:** The height of the tree is $3$ meters.