1. The problem involves finding unknown side lengths (hypotenuses or legs) of right triangles using the Pythagorean theorem. 2. Recall the Pythagorean theorem: $$a^2 + b^2 = c^2$$ where $a$ and $b$ are legs, and $c$ is the hypotenuse. 3. For each triangle, identify known sides and apply the theorem to solve for the unknown. 4. Triangle (11): Legs $7$ and $8$, find hypotenuse $c$: $$c = \sqrt{7^2 + 8^2} = \sqrt{49 + 64} = \sqrt{113} = 10.63$$ 5. Triangle (12): Leg $6$, hypotenuse $256$, find other leg $b$: $$b = \sqrt{256^2 - 6^2} = \sqrt{65536 - 36} = \sqrt{65500} = 255.98$$ 6. Triangle (13): Legs $2$ and $3$, find hypotenuse $c$: $$c = \sqrt{2^2 + 3^2} = \sqrt{4 + 9} = \sqrt{13} = 3.61$$ 7. Triangle (14): Leg $3$, hypotenuse $144$, find other leg $b$: $$b = \sqrt{144^2 - 3^2} = \sqrt{20736 - 9} = \sqrt{20727} = 143.99$$ 8. Triangle (15): Legs both $2$, find hypotenuse $c$: $$c = \sqrt{2^2 + 2^2} = \sqrt{4 + 4} = \sqrt{8} = 2.83$$ Final answers: - (11): hypotenuse $\approx 10.63$ - (12): unknown leg $\approx 255.98$ - (13): hypotenuse $\approx 3.61$ - (14): unknown leg $\approx 143.99$ - (15): hypotenuse $\approx 2.83$