Question

how do you find the length of the hypotenuse when you have only the length of the altitude of the hypotensuse and a length of a leg?

Answer 1

By using The Pythagorean Theorem:

`/Hypotenuse/^(2) = /Length of altitude/^(2) + /Length of leg/^(2) \`

/Hypotenuse/ =
`\sqrt\ /Length of altitude/^(2) + /Length of leg/^(2) \}`

Explanation:

The Pythagorean theorem states that: Given a Right-angled triangle, the square of the hypotenuse equals the sum of squares of the other two sides ( Here, being the length of the altitude and length of leg). That is,

`/Hypotenuse/^(2) = /Length of altitude/^(2) + /Length of leg/^(2) \` and hence,

/Hypotenuse/ =
`\sqrt\ /Length of altitude/^(2) + /Length of leg/^(2) \}`

For example, If the length of the altitude is 4m and the length of leg is 3m. Using The Pythagorean theorem, the length of the hypotenuse will be

`/Hypotenuse/^(2) = /Length of altitude/^(2) + /Length of leg/^(2) \\\/Hypotenuse/ = \sqrt{/Length of altitude/^(2) + /Length of leg/^(2)} \\/Hypotenuse/ = \sqrt{4^(2) + 3^(2) }`

`/Hypotenuse/ = √(16+9) \\/Hypotenuse/ = √(25) \\/Hypotenuse/ = 5m`

The length of the hypotenuse for the given example will be 5m.

This is how to find the length of an hypotenuse.