1. The problem is to find the length of the hypotenuse of a right triangle using Pythagoras' theorem or basic trigonometry. 2. Pythagoras' theorem states that in a right triangle, the square of the hypotenuse $c$ is equal to the sum of the squares of the other two sides $a$ and $b$: $$c^2 = a^2 + b^2$$ 3. To find $c$, take the square root of both sides: $$c = \sqrt{a^2 + b^2}$$ 4. If you know the lengths of the two legs $a$ and $b$, plug them into the formula and calculate $c$. 5. For example, if $a=3$ and $b=4$, then $$c = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5$$ 6. This means the hypotenuse length is 5 units. 7. Alternatively, if you know one leg and an angle, you can use trigonometry: $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$ or $$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$$ to find the hypotenuse. 8. But Pythagoras' theorem is the simplest and most direct method when both legs are known.