- #1
TytoAlba95
- 132
- 19
- Homework Statement
- See below
- Relevant Equations
- See below
Where did I go wrong?
So of the four potential answers, only two of them should be considered.Delta2 said:(hint: the triangle is isosceles)
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.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.
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 said:I had another reasoning in my mind using the cosine law.
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.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.
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.
No it isnt. Using the triangular inequality is probably the simplest way.Office_Shredder said:That's not exactly the simplest way to prove 6 is the upper bound.
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.
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).
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.
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.
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.