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

Answer:

By using The Pythagorean Theorem:

$/Hypotenuse/^{2} = /Length of altitude/^{2} + /Length of leg/^{2}$

/Hypotenuse/ = $\sqrt\ /Length of altitude/^{2} + /Length of leg/^{2} \}$

Step-by-step 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

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

$/Hypotenuse/ = \sqrt{16+9} \\/Hypotenuse/ = \sqrt{25} \\/Hypotenuse/ = 5m$

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

This is how to find the length of an hypotenuse.