Question

The hypotenuse of a right triangle is 103.1 and one leg is 40. What is the other leg?

Answer 1

`b=95.02`

Explanation:

The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. The equation that represents this relationship is:

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

where `c` is the hypotenuse and `a` and `b` are the other two sides.

We know `c` and one of the other legs, which I'll designate as `a`. So we need to find side `b`.

Rearrange the equation to isolate `b^2`, substitute the given values into the equation and solve.

`b^2=c^2-a^2`

`b^2=(103.1)^2-40^2`

`b^2=9029.61`

Take the square root of both sides.

`b=sqrt(9029.61)=95.02`