Question

8 ft
6 ft
what is the length of the hypotenuse?
ft

Explanation:

Step1: Identify the formula

For a right - triangle, we use the Pythagorean theorem, which is $a^{2}+b^{2}=c^{2}$, where $a$ and $b$ are the legs of the right - triangle and $c$ is the hypotenuse. Here, $a = 8$ ft and $b=6$ ft.

Step2: Substitute the values into the formula

Substitute $a = 8$ and $b = 6$ into the formula: $8^{2}+6^{2}=c^{2}$. Calculate $8^{2}=64$ and $6^{2}=36$. Then $64 + 36=c^{2}$, so $100=c^{2}$.

Step3: Solve for c

Take the square root of both sides. Since $c$ represents a length, we take the positive square root. $\sqrt{c^{2}}=\sqrt{100}$, so $c = 10$.

Answer:

10