if they tell you two sides of a triangle, how do you find the third?

Question

all the sides are different sizes

Answer 1

That's impossible, unless you give me the perimeter, an angle or the area. The only way the third side can directly be computed is if the triangle is right-angled.

Answer 2

Given two sides of a triangle, you can find the third side provided that the angel between these two legs is also given.

To get what I mean, right now pick two pens. Put the tip together and by moving them far and near to each other.
As you see the lenght of the fisrt pen is not changed and neither is the length of the second pen.
but with increase and decrease in the angel between them, the distance between the ends of the pens has changed.
It means, even if two legs have a constant length, the third leg's length changes by the change in the value of the angel between the first two legs.

So in here my friend, you cannot calculate the length of third leg unless you know the angel between them or the angel between one of the known legs and the third leg.
If you know the angel then you can use the following formula to calculate the length of the third leg.

a² + b² - 2(a)(b)(cos x) = c²
where:
a & b are the two known legs
x is the angel between a & b.
c is the unknown leg.

if you know the angel between a known leg and an unknown leg, then use this formule
a² + c² - 2(a)(c)cos y = b²
where:
a & b are the two known legs
y is the angel between a & c.
c is the unknown leg.

As you may have noticed, this is the general case of a² + b² = c² in a right triangle.
where c is the hypotenouse,
a & be are the legs forming the 90 degree angel.
In the right triangle, the angel between a & b is 90 and
Cos(90) = 0, so the last term is usually elliminated.

By knowing only the lenght of the two legs, you cannot calculate the length of the third leg. These two legs can stretch in one direction back to back and form a straight line.
Hope you got what I mean.

Good Luck !

Answer 3

It depends on what kind of triangle it is.. Usually, the right triangle is the easiest. You would use the pythagorean theorem. The pythagorean theorem is:

a^2+b^2=c^2, with c being the hypotenuse, or the opposite side of the right angle. Use this formula to find the missing side of a right triangle

Answer 4

You need to know at least one other piece of information. You can't solve a triangle with just 2 bits of info. If you're triangle is a right triangle and you aren't telling us, you just use the Pythagorean theorem.

Answer 5

You can't find a definite length. It is bound by the following conditions: for known sides x and y, x being the longer of the two sides, and z the unknown side:

x - y < z < x + y

Answer 6

You dont!You need three quantities to define a triangle; all three sides ., one side plus two angles or two sides and one angle.If you have all three angles, you cannot construct a unique triangle , only similar ones..

Answer 7

You must have exactly one more piece of information, specifically one of the angles. If the angle is between the given lines, the solution is unique; if it is at the end of one of them, there may be two solutions, one, or none.

Answer 8

You must know the angle between the sides. Else it cannot be solved

Answer 9

you need to know one angle to use this:

SOH (sine: opposite over hypotenuse)

CAH (cosine: adjacent over hypotenuse)

TOA (tangent: oppostite over adjacent)

ps the answer above mine is for a right angled triangle - just saw it now

Answer 10

A squared + B squared = C squared