Converse of the Pythagorean Theorem: For a triangle with given side lengths, determine if the measure of the largest angle is 90° or = 90°: 5,6,8 a. 90° c. = 90°: d. Cannotbedetermined

Question

Converse of the Pythagorean Theorem: For a triangle with given side lengths, determine if the measure of the largest angle is < 90°, > 90° or = 90°: 5,6,8 a. <90° b. >90° c. = 90°: d. Cannotbedetermined

anonymous · Answer

i dont understand this can someone explain and help pls

anonymous · Answer

@e.mccormick @rishavraj @thadyoung @Ashleyisakitty @dan815 @Callisto @bibby

anonymous · Answer

the sides are 5,6 and 8

anonymous · Answer

I'm pretty sure that its a @e.mccormick

e.mccormick · Answer

OK, what they are wantin you to do is square all three numbers and see if the sum of the smaller two is < = > the larger one.

anonymous · Answer

ya because the legs value is smaller than the hypotenuse so that makes it an acute triangle right?

e.mccormick · Answer

5, 6, 8 square to 25, 36, 64

25+36 = 61

Yah, so smaller than a $90^\circ$

anonymous · Answer

yay :) thank you can u help with one more cause i don't understand it at all

e.mccormick · Answer

Or...  hmmm...  wait a second... that may actually be B.

anonymous · Answer

oh

e.mccormick · Answer

See, if it WAS a right triangle, the hypotenuse would be 61!

anonymous · Answer

yes

e.mccormick · Answer

64 is more than 61, so the 8 side is longer than the right trianngles hypotenuse.

anonymous · Answer

but the hypotenuse is greater than the legs

anonymous · Answer

oooo so it would be an obtuse?

e.mccormick · Answer

Compared it the wrong way the first time...

e.mccormick · Answer

yah.

|dw:1426227891339:dw|

because that is a square, it is obviously right...

e.mccormick · Answer

Here is what happens when thr square of the hypotenuse is greater.
|dw:1426227922746:dw|

anonymous · Answer

oohhhhh i get it now

e.mccormick · Answer

And when it is less...
|dw:1426227987384:dw|

anonymous · Answer

so its more than 90 degrees

e.mccormick · Answer

yah.  So if $a^2+b^2=c^2$ it is the right triangle.

$a^2+b^2<c^2$ obtuse because the hypotenuse is too long for the legs of a right.

$a^2+b^2>c^2$ accute because the hypotenuse it too short for the legs of a right.

e.mccormick · Answer

Glad I caught that quick... hehe.  I did it the backwards way too.  But when you think about it, this is how it has to work!

anonymous · Answer

oh okay thank you :) i have one more could u help with that one?

e.mccormick · Answer

Well, I need to head to bed...