Question

The length of one leg of a right triangle is 6 and the length of the hypotenuse is 23. Find the length of the missing leg to the nearest hundredth.

Answer 1

The length of the missing leg is 22.20.

Explanation:

You can use the Pythagorean theorem to solve for the length of the missing leg:

`a^(2)` +
`b^(2)` =
`c^(2)`, where a and b are the lengths of the legs and c is the length of the hypotenuse.

First, substitute the lengths of the given values:

`6^(2)` +
`b^(2)` =
`23^(2)`

Next, simplify the exponents on both sides:

36 +
`b^(2)` = 529

Then, isolate b by subtracting 36 from both sides:

`b^(2)` = 493

Next, take the square root of both sides:

b =
`√(493)`

Finally, take the square root and round according to the given directions:

b = 22.20