1. **Stating the problem:** We have a ladder 3.5 m long leaning against a wall. (a) Find the height the ladder reaches on the wall when the base is 1.2 m from the wall. (b) Find the distance from the wall where the ladder must be placed to reach 3 m height. 2. **Formula used:** We use the Pythagorean theorem for right triangles: $$a^2 + b^2 = c^2$$ where $c$ is the hypotenuse (ladder length), $a$ is the height on the wall, and $b$ is the distance from the wall. 3. **Part (a) calculation:** Given $c=3.5$ m and $b=1.2$ m, find $a$: $$a = \sqrt{c^2 - b^2} = \sqrt{3.5^2 - 1.2^2}$$ Calculate inside the root: $$3.5^2 = 12.25, \quad 1.2^2 = 1.44$$ So: $$a = \sqrt{12.25 - 1.44} = \sqrt{10.81}$$ Calculate the square root: $$a \approx 3.29 \text{ m}$$ 4. **Part (b) calculation:** Given $c=3.5$ m and $a=3$ m, find $b$: $$b = \sqrt{c^2 - a^2} = \sqrt{3.5^2 - 3^2}$$ Calculate inside the root: $$3.5^2 = 12.25, \quad 3^2 = 9$$ So: $$b = \sqrt{12.25 - 9} = \sqrt{3.25}$$ Calculate the square root: $$b \approx 1.80 \text{ m}$$ **Final answers:** (a) The ladder reaches approximately $3.29$ m height on the wall. (b) The ladder base must be placed approximately $1.80$ m from the wall to reach 3 m height.