How to calculate the length of the side of a triangle?

[Scott M]

I was wandering If some one could help me with this formula
I need to find the length of 1 side of a triangle when the longest side is known and the angle is known
for example the longest side is 16 inches and the angle is 90 deg.
http://screencast.com/t/7qENS4FCN

 

[theBardd]

I think you would need at least one more angle or length to get that.

 

[James006]

Hi,

Basically, it is the Pythagorean theorem : <dl style="margin-top: 0.2em; margin-bottom: 0.5em; color: rgb(0, 0, 0); font-family: sans-serif; line-height: 19.1875px;"><dd style="line-height: 1.5em; margin-left: 1.6em; margin-bottom: 0.1em; margin-right: 0px;">

</dd></dl>where c represents the length of the hypotenuse ( the longest side), and a and b represent the lengths of the other two sides.

Cheers

 

[Cool blue]

It can be whatever you like. You need one more constraint to force a unique solution.

 

[Scott M]

I think you would need at least one more angle or length to get that.

The angle at the bottom left is 45 Deg. To the longest side (16")
2013-12-30_0913 - ScottMarshburn's library

 

[theBardd]

That original picture isn't 45 deg, but if the triangle is 45 and 45, each other side is simply

=SQRT(16^2/2)

 

[James006]

Just the square root of 128 ...

 

[RoryA]

For other angles, the side to the left (adjacent) is:
=COS(RADIANS(angle))*hypotenuse
and the opposite side is:
=SIN(RADIANS(angle))*hypotenuse

 

[mikerickson]

The Pythagorean theorm applies only to right triangles. A more general formula that works with any angle is the Law Of Cosines
Given a triangle where sides A, B and C are across from angles a, b, and c, the Law of Cosines says that

A^2 = (B^2)+(C^2) - (2*B*C*Cos(a))

(Note that if a is a right angle, this becomes the pythagorean theorem.)

There is also the triple equality called the Law Of Sines

A/Sin(a) = B/Sin(b) = C/Sin(c)

With these two equations (and enough information), any triangle can be solved.

 

[Scott M]

Thank you all for your help. With the information that you provided I think that I can for sure accomplish what I want.