Question

A triangle has side lengths 10, 15, and 7. Is the triangle acute, obtuse, or right? Explain

Answer 1

Use Pythagoras.
\[a^2 + b^2 = c^2\]

Answer 2

If they coincide, and relate, the triangle is a right angle.

Answer 3

so it would be 10^2 + 15^2 = what ??

Answer 4

If they don't it's either going to be acute or obtuse. For it to be acute, the hypotenuse of a right angle triangle is longer than your given hypotenuse which is 15 it is acute. If not, then it's obviously left with the only option to be obtuse.

Answer 5

c in that equation is the hypotenuse.

Answer 6

i dont get what numbers to put in which letters
Im SO CONFUSED

Answer 7

the two shortest lengths of the triangle correspond with a^2 and b^2

Answer 8

the longest side which is 15, is the hypotenuse of the triangle.

Answer 9

okay so 7^2 + 10^2 = 149
So Now What

Answer 10

Now c^2= 149, am I right?

Answer 11

No c^2 = 225

Answer 12

Now all you have to do is Find c, which is around 12.2 and the longest length given in your question is 15. So the ideal right angle triangle with the two shortest sides you were given in the question has to have a hypotenuse of 12.2

Answer 13

225?....Are you drinking anything that's giving your problems with your thinking process?

Answer 14

giving you*

Answer 15

well wouldnt it be 15^2 = 225 ? i dont know im confused

Answer 16

You're jumping ships at the moment. Right now c^2 is 149. You're thinking about the longest side given in your question.

Answer 17

Don't do that just yet. Stay at what you're doing right now. Take mathematics as a step by step process.

Answer 18

If you ruin the steps and just jump ahead two steps further, you're going to be in trouble if you do this in exams.

Answer 19

okay so were saying a+b = 149 and c = 149 //

Answer 20

No,
\[a^2 + b^2= 149\]

Answer 21

c^2= 149.
c=? HINT: Use your calculator.

Answer 22

okay i get it

Answer 23

whats next

Answer 24

Okay so, you end up with 12.2 (to the nearest dcp.) So for an ideal right angled triangle, your hypotenuse must have a length of 12.2

Answer 25

that's with the dimensions of 7, 10 that you were given in the question.

Answer 26

Now in the question, you have a triangle that has an hypotenuse of 15 instead of 12.2

Answer 27

That tells you that it's not a right angled triangle. Therefore your only options are that the triangle must be acute or obtuse.

Answer 28

You with me?

Answer 29

yea im with you sorry my nephew is being bad lol . keeep going

Answer 30

Okay. So if your given hypotenuse is less than 12.2 (eg. your dimensions were 7,10 and 11) then the triangle is acute.

Answer 31

But you were given dimensions of 7, 110 and 15.

Answer 32

10*

Answer 33

Okay so its not acute or right. So it would be obtuse ?

Answer 34

so it's not acute, thus it must be obtuse.

Answer 35

Yes. Good.

Answer 36

okay can you explain how tho?

Answer 37

A triangle can aeither be acute,right angled or obtuse
as seen from Aztec's proof it is neither right angled nor zcute so it must definitely be obtuse!!

Answer 38

but i need to explain how it is an obtuse in a shorter term

Answer 39

This question only gave you three options. You can't say it's neither acute, obtuse or right angled because that's not an option. That's an aspect you should also work on is knowing your options.

Answer 40

This question does not need any further analysis because you already solved it. If the question gave you dimensions of 7,10 and 11, you would do the same process. You would then find that the hypotenuse of the triangle (ie. side length of 11) is shorter than the ideal hypotenuse of a right angled triangle which is 12.2. Therefore you say that it's acute because it's shorter than the ideal hypotenuse of 12.2 in a right angled triangle

Answer 41

If you still want to understand more about this. This link gives you everything you need.
http://www.algebra.com/algebra/homework/Triangles/Triangles.faq.question.457725.html