Step 1. Define the hypotenuse of the triangle as "c":
[tex]c=10m[/tex]Step 2. Define the known leg of the right triangle as "a":
[tex]a=8m[/tex]Step 3. We will use the Pythagorean theorem to solve the problem.
The Pythagorean theorem relates the hypotenuse c of a right triangle, with its legs a and b as follows:
[tex]a^2+b^2=c^2[/tex]So we can substitute the known values for a and c:
[tex](8m)^2+b^2=(10m)^2[/tex]Solving the exponents:
[tex]64m^2+b^2=100m^2[/tex]Step 4. Solve to find the value of b (the other leg of the triangle).
To solve for b, first, we subtract 64m^2 to both sides of the equation:
[tex]b^2=100m^2-64m^2[/tex]And we get:
[tex]b^2=36m^2[/tex]The last step to solve for b, is to take the square root of both sides of the equation:
[tex]\sqrt[]{b^2}=\sqrt[]{36m^2}[/tex]On the left side we get "b":
[tex]b=\sqrt[]{36m^2}[/tex]And on the right side, we get 6m:
[tex]b=6m[/tex]Answer: 6m
