Question

Find the length of the sides of a triangle?

Asked by: DJ_AM_Juicebox

Hi,

I have a triangle, I know the measures of all its angles, and the length of the hypotenuse. I need to find the lengths of the other two sides. What formula can I use to get that?

Thanks, I tried to put a diagram below:

b
                /
              /  |
            /    |
          /      |
        /        | 
 a    ---------  c
 
a = 45
b = (180 - (a+c))
c = 90 (always)
 
Hypotenuse = 1 (always)
What are the other 2 sides?

                                  
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Asked On
2009-09-15 at 08:47:41ID24733359
Topic

Math & Science

Participating Experts
6
Points
500
Comments
12

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Answers

 

by: sdstuberPosted on 2009-09-15 at 08:59:45ID: 25336341

looks like homework,
hint - use Pythgorean theorem



 

by: jparkerscPosted on 2009-09-15 at 09:01:31ID: 25336358

The diagram you gave is a right triangle and it uses it own rules but one way to solve any triangle is to use the two equations:

Assuming A, B, abd C are the interior angles and a, b, and c are the side lengths of the sides opposite the interior angles

Sum of internal angles -  A + B + C = 180 degrees  (If you know any two angles you can calculate the third)

Rule of sines - a/sineA = b/sineB = c/sineC (The sine rule is easier than the cosine rule.)

You can develop your own equations for solving but here is a website that explains it easily.

http://www.wikihow.com/Use-the-Sine-Rule

 

by: DJ_AM_JuiceboxPosted on 2009-09-15 at 09:02:11ID: 25336369

It's not homework, I have to make a Snood game and I need to know how much to update the x,y position of the fired element on each game frame, depending on the angle of the canon.

Doesn't pythagoerean only give a2 + b2 = c2?

Thanks

 

by: jkunreinPosted on 2009-09-15 at 09:04:22ID: 25336390

Since c always equals 90, you have a right triangle.  There are some easy ways to calculate the lengths of the triangle.  

You know the Pythagorean Theorem...use that, but consider what happens when the two sides are equal (which is the case if their opposite angles are equal).

 

by: jkunreinPosted on 2009-09-15 at 09:07:00ID: 25336420

Also, you can use SOHCAHTOH for any right triangle (link: http://en.wikipedia.org/wiki/Trigonometry).

That can also be used here, but in a 90-45-45 triangle, there is a relationship between the lengths of the sides and the length of the hypotenuse.  Though, it looks like your a is variable, so that relationship doesn't always work.  But, SOHCAHTOH will work for any right triangle.

 

by: jparkerscPosted on 2009-09-15 at 09:09:40ID: 25336443

The sine rule will work for any triangle, not just right triangles.  If you are only working with right triangles then the Pythagorean Theorem will be an easier calculation in a program.

 

by: jkunreinPosted on 2009-09-15 at 09:16:39ID: 25336518

The Pythagorean Theorem is easy to use for right triangles where two side lengths are known.  It looks like the original question contains a triangle where all three angles are known, as well as the length of the hypotenuse.  In that case, the sine rule would have to be used (or any derivatives of that).

But if you known two side lengths, the Pythagorean Theorem is by far the easiest route to take.

 

by: JerksonPosted on 2009-09-15 at 09:16:40ID: 25336519

Using the "Law of Sines"

Sin a / A  = Sin b / B = Sin c / C

So in your case:
Sin 90 / 1  =  Sin 45 / x

Solving for X...
x = 0.70710678118

so your side b-c is .707


so the same for side a-c using angle B

 

by: sdstuberPosted on 2009-09-15 at 09:18:02ID: 25336538

yes

a^2 + b^2 = c^2  

but  in the formula's case the a,b,c refer to the length of the sides not the angles as you have them labeld.

But if you substitute each side opposite it's corresponding angle it will work just fine.

so ...

since a=b   you can reduce the formula to

a^2 + a^2 = 1

2a^2 = 1

a^2  = 1/2

a=    1 / (sqrt(2))  or approx  0.7071

 

by: aburrPosted on 2009-09-15 at 09:18:06ID: 25336540

jparkersc gave you the answers.
In detail
Let angle be cap letter and side opposite be small letter.
Because you have right triangle C = 90 degrees and sineC=1. You know A,B,C.
from jparkersc

a/sinA = c/sinC      therefore     a = C sineA
and similarly                               b = C sineB

 

by: NovHakPosted on 2009-09-15 at 09:31:06ID: 25336683

The present case is fairly easy, no need to compute any sine or cosine (even if the values are well known here).

A=45°, C=90° then B=45° so A=B, hence CA=CB. Thanks to the Pythagorean theorem, we know that AB²=CA²+CB², hence AB²=2CA², hence 2CA²=1, so CA=CB=sqrt(2)/2.

Here is the more general solution (with A and B varying, and C=90°), which can be derived from the sines rule, with C=90° :

CA=ABcos(A)=ABsin(B)
CB=ABcos(B)=ABsin(A)

HTH,

NH

 

by: DJ_AM_JuiceboxPosted on 2009-09-15 at 09:33:56ID: 25336704

Ah great, ok I just did this:

       double r = Math.Sin(MathHelper.ToRadians(90)) / 1.0f;
       double a = Math.Sin(MathHelper.ToRadians(mRotationCannon)) * r;
       double b = Math.Sin(MathHelper.ToRadians(180 - (90 + mRotationCannon))) * r;

Thanks

20120131-EE-VQP-002

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