One of the legs of a right-angled triangle is 8/17 m, and the hypotenuse is 10 dm. Find the second leg.

Apparently, there is an error in the task, since 8/17 m> 10 dm. But the leg cannot be larger than the hypotenuse by definition. Most likely, it meant 8/17 dm. Let’s solve the problem based on this assumption:

According to the Pythagorean theorem, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse:

a ^ 2 + b ^ 2 = c ^ 2,

whence the length of one of the legs is

a = sqrt (c ^ 2 – b ^ 2).

For a given triangle, the length of the unknown leg is

a = sqrt (10 ^ 2 – (8/17) ^ 2) = sqrt (100 – 64/289) = sqrt (28836/289) = 18 * sqrt (89) / 17.