Question

find the value of b. pythagorean theorem: a² + b² = c²

Explanation:

Step1: Identify the Pythagorean theorem components

In a right - triangle, if the hypotenuse is $c$ and the other two sides are $a$ and $b$, the Pythagorean theorem is $a^{2}+b^{2}=c^{2}$. Here, $a = 7m$, $c = 10m$, and we need to find $b$.

Step2: Rearrange the Pythagorean formula

We can rewrite the formula as $b^{2}=c^{2}-a^{2}$. Substitute $a = 7$ and $c = 10$ into the formula: $b^{2}=10^{2}-7^{2}$.

Step3: Calculate the values

$10^{2}=100$ and $7^{2}=49$. So $b^{2}=100 - 49=51$.

Step4: Solve for $b$

$b=\sqrt{51}$ m.

Answer:

$b = \sqrt{51}$ m