Probability obtuse triangle - simple one

[wuid]

Homework Statement

The two sides lengths of a triangle is exponentially distributed. (not so important for my question)

The angle between the sides is uniformly distributed [0,2∏]

c) explain why the probability to get obtuse triangle is greater then 0.5

The Attempt at a Solution

i don't understand why it is grater then 0.5 and not exactly 0.5...

 

[I like Serena]

Homework Statement

The two sides lengths of a triangle is exponentially distributed. (not so important for my question)

The angle between the sides is uniformly distributed [0,2∏]

c) explain why the probability to get obtuse triangle is greater then 0.5

The Attempt at a Solution

i don't understand why it is grater then 0.5 and not exactly 0.5...

Hi wuid!

Looks like the question is the probability to get any obtuse angle in the triangle (also considering the other 2 angles)...

 

[wuid]

i am missing something... to get obtuse triangle is that the probability of the angle to be between [∏/2,3∏/2] so what i thought is : what is the probability that θ is within the II or III quarter of the plane so it is P(II)+P(III) = 0.25 + 0.25 = 0.5.

where i am wrong ?

 

[I like Serena]

What about the other 2 angles of the triangle?

Suppose your angle is acute, but one side is very long while the other side is very short.
What kind of triangle would you have?

 

[wuid]

obtuse triangle :)
so without calculation, can i say that the probability is greater than 0.5, because that i get obtuse angle with probability 0.5 but i need to add a measure of probability that the other two angles would sum up with the first on to 180 degrees ? gives that the triangle is obtuse.

 

[I like Serena]

Yep!

 

[wuid]

I never see the all picture...
thank you !

 

[I like Serena]

You're welcome!