Do 3-4-5 Triangles Have to be 30-45-90?

[Bradracer18]

Homework Statement

Hey, I have quick question. I tried looking on google, but couldn't quite reassure myself.

Does a 3-4-5 triangle have to be a 30-45-90 triangle? Can the angles be any angle?(this is what I think...but not confident).

I have a triangle(this is actually a physics problem)...but the triangle has a leg which is 3' and a leg that is 4'...so the hyp must be 5'...but i need to know the angles.

Homework Equations

The Attempt at a Solution

 

[robphy]

Homework Statement

Hey, I have quick question. I tried looking on google, but couldn't quite reassure myself.

Does a 3-4-5 triangle have to be a 30-45-90 triangle? Can the angles be any angle?(this is what I think...but not confident).

No, a 3-4-5 triangle does not have a 30 or 45 degree angle.
No.

I have a triangle(this is actually a physics problem)...but the triangle has a leg which is 3' and a leg that is 4'...so the hyp must be 5'...but i need to know the angles.

what is the definition of the trigonometric functions: sine, cosine, and tangent?

 

[ZioX]

There exists no triangle with 30-45-90 angles. The sum of the angles must be 180.

It should be noted that the majority of sine, cosine and tangent arguments only work for right angled triangles.

It's not necessarily true that a RIGHT triangle with 3 inch and a 4 inch lengths will have another side of length 5. How do you know that 4 isn't the hypoteneuse?

 

[AlephZero]

Does a 3-4-5 triangle have to be a 30-45-90 triangle?

The angles of a triangle add up to 180 degrees, so a 30-45-90 triangle is impossible.

Can the angles be any angle?(this is what I think...but not confident).

No, if you have the length of all 3 sides, the 3 angles are fixed.

You can find the angles of any shape of triangle using the cosine rule, if you know all three sides. For a 3-4-5 triangle, you know one angle is right angle, so you can save time and use the definitions of sine and cosine instead of using the full cosine rule.

 

[Bradracer18]

I have a picture...I guess I'm having a brain fart...

I know there is a 90 deg angle(where the 3 and 4 sides meet,angle opposite from the hyp)...so then, can't i use the law of sines to find the angles?

I know the def's of trig functions...what does that help...opp/adj...opp/hyp...adj/hyp...

 

[robphy]

I know the def's of trig functions...what does that help...opp/adj...opp/hyp...adj/hyp...

What specifically is equal to "opp/adj"? etc...

 

[Bradracer18]

ok...so can't I just do this...

sin90/5 = sinx/3 which I think gives me a 36.87 deg angle. This is what I came up with in the begining...just didn't seem right.

 

[Bradracer18]

tan = opp/adj...or I think its also sin/cos(or something like that...y/x?)...definitely know its tan.

 

[AlephZero]

I know there is a 90 deg angle(where the 3 and 4 sides meet,angle opposite from the hyp)...so then, can't i use the law of sines to find the angles?

Yes, that's yet another way to do it if you don't like the other suggestions.

 

[Bradracer18]

ok...well I think I've got it then...thanks all! A nice brush up on my trig skills...ha