Find the third side of a Triangle

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In summary: No it isnt. Using the triangular inequality is probably the simplest way.I actually needed the simplest, or more precisely the shortest method to answer this question, as I was preparing for a MCQ-based exam.
  • #1
TytoAlba95
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Homework Statement
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Relevant Equations
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Where did I go wrong?
 
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  • #2
From where do you know that that angle is 60 degrees? We have no explicit information on the angles of the triangle, so how did you infer it from the given data?

Instead try to think what are the possible values for the third side (hint: the triangle is isosceles) and try to find a reason to reject one value so you ll be left with the other.
 
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  • #3
Delta2 said:
(hint: the triangle is isosceles)
So of the four potential answers, only two of them should be considered.
 
  • #5
The other side can be between, (7+3=)10 and (7-3=)4 cm, being an isosceles triangle, the third side should be either 7 or 3. As 3 is below the range so 7cm is the length of the other side. Thanks for the pointer.
 
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  • #6
TytoAlba95 said:
The other side can be between, (7+3=)10 and (7-3=)4 cm, being an isosceles triangle, the third side should be either 7 or 3. As 3 is below the range so 7cm is the length of the other side. Thanks for the pointer.
Very well i find your reasoning correct. You used the triangular inequality. I had another reasoning in my mind using the cosine law. Let me know if you want to hear it.
 
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  • #7
Delta2 said:
I had another reasoning in my mind using the cosine law.
Which is fine, but requires calculation that probably can't be done in one's head. A variation of the technique used by the OP is to draw two isosceles triangles: one with two sides of 3 units, and the other with two sides of 7 units. Pretty clearly the one with a pair of sides of 3 units can't also have a side of 7 units, but the one with a pair of 7 unit sides can have a third side of 3 units.
 
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Mark44 said:
Which is fine, but requires calculation that probably can't be done in one's head. A variation of the technique used by the OP is to draw two isosceles triangles: one with two sides of 3 units, and the other with two sides of 7 units. Pretty clearly the one with a pair of sides of 3 units can't also have a side of 7 units, but the one with a pair of 7 unit sides can have a third side of 3 units.
It is not that hard. Take a triangle isosceles with two sides of 3. We can prove using the cosine law that the third side has an upper bound of 6.
 
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  • #9
Delta2 said:
It is not that hard. Take a triangle isosceles with two sides of 3. We can prove using the cosine law that the third side has an upper bound of 6.

That's not exactly the simplest way to prove 6 is the upper bound.
 
  • #10
Office_Shredder said:
That's not exactly the simplest way to prove 6 is the upper bound.
No it isnt. Using the triangular inequality is probably the simplest way.
 
  • #11
I actually needed the simplest, or more precisely the shortest method to answer this question, as I was preparing for a MCQ-based exam.
Thank you everyone for your pointers and inputs. Thank you Delta2. :)
 
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1. What is the formula for finding the third side of a triangle?

The formula for finding the third side of a triangle is the Pythagorean theorem, which states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

2. How do you use the Pythagorean theorem to find the third side of a triangle?

To use the Pythagorean theorem, you need to know the lengths of two sides of the triangle. Simply plug these values into the formula a² + b² = c², where a and b are the lengths of the two known sides, and c is the length of the unknown side (third side).

3. Can you find the third side of any triangle using the Pythagorean theorem?

No, the Pythagorean theorem only applies to right triangles, which have one angle measuring 90 degrees. For other types of triangles, you would need to use different formulas to find the missing side length.

4. What if I only know the length of one side and the angles of a triangle, can I still find the third side?

Yes, you can use the law of sines or the law of cosines to find the missing side length in this scenario. These formulas take into account the angles of the triangle and the length of one side to calculate the length of the other sides.

5. Is there a way to check if I have correctly found the third side of a triangle?

Yes, you can use the triangle inequality theorem to check if the length of the third side you found is possible. This theorem states that the sum of any two sides of a triangle must be greater than the length of the third side. If this condition is not met, then the lengths you have found are not possible for a triangle.

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