Question

Show work to triangles 2 and 3 explaining why they are right triangles

Answer 1

Answer:

Step-by-step explanation:

In order for a triangle to be a right triangle, it has to fit into Pythagorean's Theorem:

$a^2+b^2=c^2$ where c is the hypotenuse.

We need to figure out which is the longest side in each of those triangles and that is the hypotenuse.

In the first set, the sqrt of 443 is 21.04, but that is not the longest side; 24 is. So the Theorem formula for that is:

$\sqrt{443}^2+17^2=24^2$ which gives us

443 + 289 = 576, but 732 does not equal 576, so that one is not right.

In the second set, the sqrt of 725 is the longest side, so that formula is:

$\sqrt{725}^2=14^2+23^2$ which gives us

725 = 196 + 529, and 725 does equal 725, so that one is right.

In the third set, the sqrt of 890 is the longest side, so:

$\sqrt{890}^2=19^2+23^2$, which gives us

890 = 361 + 529, and 890 = 890, so that is a right triangle as well. That's how you know those are right, compared to the first one that is not.