Question

missing side = _ ft. missing side = _ in. missing side = ___ cm

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with sides $a$, $b$ and hypotenuse $c$, $a^{2}+b^{2}=c^{2}$. If we know two sides, we can find the third.

Step2: First triangle (8 ft side and unknown side)

Let the unknown side be $x$ and assume the 8 ft side is one of the legs. If the hypotenuse is $h$, and the other leg is $x$, and we assume $h$ is unknown. But if we assume the given side is a leg and we want to find the other leg, and no hypotenuse is given, this part of the problem seems incomplete. Let's move to the second triangle.

Step3: Second triangle (13 in and 12 in sides)

Let $a = 12$, $c=13$. Using the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, we can find the other leg $b$. Rearranging for $b$, we get $b=\sqrt{c^{2}-a^{2}}$. Substitute $a = 12$ and $c = 13$: $b=\sqrt{13^{2}-12^{2}}=\sqrt{169 - 144}=\sqrt{25}=5$ in.

Step4: Third triangle (5 cm and 6 cm sides)

Let the sides of the right - triangle be $a = 5$ and $b = 6$. If we want to find the hypotenuse $c$, then $c=\sqrt{a^{2}+b^{2}}=\sqrt{5^{2}+6^{2}}=\sqrt{25 + 36}=\sqrt{61}\approx 7.81$ cm.

Answer:

Second triangle: 5 in
Third triangle: $\sqrt{61}\approx7.81$ cm