Find the third side of a Triangle

[TytoAlba95]

Homework Statement

See below

Relevant Equations

See below

Where did I go wrong?

 

[Delta2]

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.

 

[Mark44]

(hint: the triangle is isosceles)

So of the four potential answers, only two of them should be considered.

 

[Lnewqban]

Please, see:
https://en.wikipedia.org/wiki/Isosceles_triangle

 

[TytoAlba95]

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.

 

[Delta2]

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.

 

[Mark44]

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.

 

[Delta2]

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.

 

[Office_Shredder]

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.

 

[Delta2]

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.

 

[TytoAlba95]

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. :)