1. **Stating the problem:** Calculate lengths WY and XY in a right-angled triangle XYZ with right angles at W and Z. 2. **Given:** - WZ = 4 cm (vertical) - ZY = 7.5 cm (horizontal) - WX = 2 cm (vertical) - Hypotenuse XY is unknown and needs to be found. 3. **Finding WY:** Since WZ and WX are vertical segments, WY is the total vertical length combining WX and WZ: $$WY = WZ - WX = 4 - 2 = 2 \text{ cm}$$ 4. **Finding XY:** The hypotenuse XY can be calculated using the Pythagorean theorem in triangle WXY. Segment WY is vertical and ZY is horizontal but to find XY we use the total vertical segment WY (2 cm) and horizontal segment ZY (7.5 cm): $$XY = \sqrt{WY^2 + ZY^2} = \sqrt{2^2 + 7.5^2} = \sqrt{4 + 56.25} = \sqrt{60.25}$$ Calculate the square root: $$XY \approx 7.8 \text{ cm}$$ (to 1 decimal place) **Final answers:** - WY = 2 cm - XY = 7.8 cm