A triangle has side lengths of 10, 24, and 30. What type of triangle is it?

Question

mathstudent55 · Answer

|dw:1379940920629:dw|

mathstudent55 · Answer

If you had a right triangle with legs of lengths 10 and 24, can you calculate what the hypotenuse length would be?

anonymous · Answer

i dont need a number i just need to know what type triangle it wud be

mathstudent55 · Answer

That's what we are getting to.
Can you answer the question?
You'll get your answer very soon.

anonymous · Answer

i got sqrt676

anonymous · Answer

100+576=900

mathstudent55 · Answer

Great.

$\sqrt{676} = 26$

mathstudent55 · Answer

If you had a right triangle with legs 10 and 24, the hypotenuse would be 26.
|dw:1379941954308:dw|

mathstudent55 · Answer

Your third side is not 26, it is greater than 26. It is 30
Let's modify the triangle to make the sides of 10 and 24 have a third side of 30.

mathstudent55 · Answer

|dw:1379942067719:dw|

mathstudent55 · Answer

In order to do so, we had to "open up" the right angle to a larger measure.
Now you can see what kind of triangle it is.

mathstudent55 · Answer

The above leads to the following rule:

In a triangle with sides a, b, and c

If $a^2 + b = c^2$, the triangle is a right triangle.
If $a^2 + b^2 < c^2 $, the triangle is an obtuse triangle. (our case, drawing above)
If $a^2 + b^2 > c^2$, the triangle is an acute triangle. (see drawing below)

mathstudent55 · Answer

|dw:1379942344539:dw|