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

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In summary, the conversation discusses the properties of a 3-4-5 triangle and the possibility of it being a 30-45-90 triangle. It is determined that a 30-45-90 triangle is not possible and the angles of a triangle are fixed if the lengths of all three sides are known. The use of trigonometric functions and the law of sines are also mentioned as methods for finding the angles of a triangle.
  • #1
Bradracer18
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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

 
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  • #2
Bradracer18 said:

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.

Bradracer18 said:
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?
 
  • #3
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?
 
  • #4
Bradracer18 said:
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.
 
  • #5
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...
 
  • #6
Bradracer18 said:
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...
 
  • #7
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.
 
  • #8
tan = opp/adj...or I think its also sin/cos(or something like that...y/x?)...definately know its tan.
 
  • #9
Bradracer18 said:
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.
 
  • #10
ok...well I think I've got it then...thanks all! A nice brush up on my trig skills...ha
 

1. Do all 3-4-5 triangles have to be 30-45-90?

No, not all 3-4-5 triangles have to be 30-45-90. A 30-45-90 triangle is a special type of right triangle where the angles measure 30 degrees, 45 degrees, and 90 degrees. A 3-4-5 triangle is simply a triangle with side lengths of 3, 4, and 5 units.

2. How do you know if a 3-4-5 triangle is a 30-45-90 triangle?

A 3-4-5 triangle is a 30-45-90 triangle if and only if the ratio of the sides follows the pattern of 3:4:5. In other words, the longest side must be twice the length of the shortest side, and the middle side must be the square root of 2 times the length of the shortest side.

3. Can a 3-4-5 triangle have different angle measures?

No, a 3-4-5 triangle will always have the same angle measures of 30 degrees, 45 degrees, and 90 degrees. This is because the angle measures of a triangle are determined by the ratio of the sides, and a 3-4-5 triangle always follows the same ratio.

4. Are all right triangles 3-4-5 triangles?

No, not all right triangles are 3-4-5 triangles. A right triangle is any triangle with one 90 degree angle, but a 3-4-5 triangle is a specific type of right triangle with specific side lengths and angle measures.

5. Can a 3-4-5 triangle have different side lengths?

No, a 3-4-5 triangle will always have the same side lengths of 3, 4, and 5 units. This is because the ratio of the sides must follow the pattern of 3:4:5 in order for the triangle to be a 30-45-90 triangle.

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