Trigonometry formula and answer

bloodhound31 · #1 28-05-2010, 05:14 PM

Hi all, I understand the principles and mechanics of how this works, I just always have a problem with the mathematical formula, and how to explain them in laymen terms.

Can anyone help with this one?

I want the formula for working out the lengths of each side, given the base and two angles are known. Plus the answer.

Cheers.

Baz.

sheeny (Al) · #2 28-05-2010, 05:29 PM

The simplest way to solve this is with the sine rule.

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

where A, B, C are the lengths of the sides and a,b and c are their opposite angles.

Remember also that the sum of the angles in a triangle = 180°

.

So the missing angle is 45° (=180-71-64).

Therefore, 5/sin(45) = B/sin(71) = C/sin(64)

Therefore, B = 6.6858259654412220511751510867703

and C = 6.3554336502823673953106682165706

Al.

Steffen · #3 28-05-2010, 05:42 PM

Quote:

Originally Posted by sheeny

So the missing angle is 55° (=180-71-64).

Or 45º, depending on your point of view

Cheers
Steffen.

bloodhound31 · #4 28-05-2010, 05:47 PM

What's sin? Besides being naughty..

Scorpius51 (John) · #5 28-05-2010, 06:00 PM

An abbreviation for the SINE of the angle in ()! Al was using the Sine Rule.

mswhin63 (Malcolm) · #6 28-05-2010, 06:01 PM

Quote:

Originally Posted by sheeny

Therefore, B = 5.7713252514678684467369091411063

and C = 5.4861246612605534554725269426624

Al.

Hope you have an accurate ruler.

sheeny (Al) · #7 28-05-2010, 06:03 PM

Quote:

Originally Posted by Steffen

Or 45º, depending on your point of view

Cheers
Steffen.

oops... yes... quite right... forgot to carry the 1...

I'll fix it.

Quote:

Originally Posted by bloodhound31

What's sin? Besides being naughty..

sin is the standard abbreviation for sine which is the ratio of the opposite side of a right triangle divided by the hypotenuse.

Al.

Scorpius51 (John) · #8 28-05-2010, 06:07 PM

Hmmm........but maybe you already knew that - I just fell for it!

hickny (Peter) · #9 28-05-2010, 06:08 PM

Barry you need a scientific calculator, one with buttons that has sin, cos, tan, on it. Sheeny has told you the correct thing. The sides and the angles opposite those sides are related by what is called the sine ratio which is abbreviated as sin.
The calculator has to be in degree mode. Generally displayed in the calculator window as either DEG or simply D.
In your image call the side opposite the side of 5m by the letter a.
Call the side opposite 71 degrees by the letter b and the side opposite 64 degrees by the letter c.
The angles in a triangle add to 180 degrees therefore the missing angle is the difference between 180 and the others added together (64+71) this gives 55 degrees.

To find side b write the ratio b/sin(71) = 5/sin(55)
Multiplying both sides of the equation by sin(71) will give you...
b=5 sin(71)/sin(55)
=5.7713252514678684467369091411063

to find c write the ratio c/sin(64) = 5/sin(55)
Muliplying both sides of the equation by sin(64) will give you...
c=5 sin(64)/sin(55)
=5.4861246612605534554725269426624
Hope that helps.

sheeny (Al) · #10 28-05-2010, 06:09 PM

Quote:

Originally Posted by mswhin63

Hope you have an accurate ruler.

yeah!

Just a straight copy out of windows calculator...

Al.

bloodhound31 · #11 28-05-2010, 06:10 PM

Quote:

Originally Posted by sheeny

sin is the standard abbreviation for sine which is the ratio of the opposite side of a right triangle divided by the hypotenuse.
Al.

What's a hypotenuse?

For example?

Please note, you are explaining this to someone who has EXTREME difficulty with this stuff.

bloodhound31 · #12 28-05-2010, 06:14 PM

Quote:

Originally Posted by hickny

To find side b write the ratio b/sin(71) = 5/sin(55)

Can you spell this out?

Is it saying divide 71 by whatever the value of sine is?

bmitchell82 (Brendan) · #13 28-05-2010, 06:17 PM

for a laymans term, use wikipedia,

google, sine rule wiki or even cosine rule they are both handy and derivations of Pythagoras's therom.

PCH (Paul) · #14 28-05-2010, 06:29 PM

Quote:

Originally Posted by bloodhound31

What's a hypotenuse?

For example?

Please note, you are explaining this to someone who has EXTREME difficulty with this stuff.

Baz,

they're large beasts that live in water-logged plains in Africa.

mithrandir (Andrew) · #15 28-05-2010, 07:13 PM

$ cat /tmp/sinerule.c
#include <stdio.h>
#include <math.h>

int main(int argc, char *argv[], char *env[]) {
long double A=5.0,B,C,Aa;
long double a,b=64.0,c=71.0,d2r;
d2r=M_PIl/180.0;
a=180.0-b-c;
Aa=A/sinl(a*d2r);
B=Aa*sinl(b*d2r);
C=Aa*sinl(c*d2r);
fprintf(stdout,"A=%0.36llf,a=%llf\n ",A,a);
fprintf(stdout,"B=%0.36llf,b=%llf\n ",B,b);
fprintf(stdout,"C=%0.36llf,c=%llf\n ",C,c);
return 0;
}

$ gcc -o /tmp/sinerule /tmp/sinerule.c -lm -D_GNU_SOURCE

$ /tmp/sinerule
A=5.0000000000000000000000000000000 00000,a=45.000000
B=6.3554336502823673953760374999433 22473,b=64.000000
C=6.6858259654412220507162245564103 38664,c=71.000000

GrahamL · #16 28-05-2010, 07:38 PM

Quote:

$ cat /tmp/sinerule.c
#include <stdio.h>
#include <math.h>

int main(int argc, char *argv[], char *env[]) {
long double A=5.0,B,C,Aa;
long double a,b=64.0,c=71.0,d2r;
d2r=M_PIl/180.0;
a=180.0-b-c;
Aa=A/sinl(a*d2r);
B=Aa*sinl(b*d2r);
C=Aa*sinl(c*d2r);
fprintf(stdout,"A=%0.36llf,a=%llf\n ",A,a);
fprintf(stdout,"B=%0.36llf,b=%llf\n ",B,b);
fprintf(stdout,"C=%0.36llf,c=%llf\n ",C,c);
return 0;
}

$ gcc -o /tmp/sinerule /tmp/sinerule.c -lm -D_GNU_SOURCE

$ /tmp/sinerule
A=5.0000000000000000000000000000000 00000,a=45.000000
B=6.3554336502823673953760374999433 22473,b=64.000000
C=6.6858259654412220507162245564103 38664,c=71.000000

Thats much clearer now Andrew

Whoa ..Paul
http://en.wikipedia.org/wiki/Hippopotamus
I didn't Know They were relitive of a doliphin that grew six axe handles across the arse
then developed an attitude.

Whats the numbers you wan't to run Baz.

GeoffW1 (Geoff) · #17 28-05-2010, 07:49 PM

Quote:

Originally Posted by bloodhound31

What's a hypotenuse?

For example?

Please note, you are explaining this to someone who has EXTREME difficulty with this stuff.

Hyppopotamus with an education?

sheeny (Al) · #18 28-05-2010, 08:15 PM

Quote:

Originally Posted by bloodhound31

What's a hypotenuse?

For example?

Please note, you are explaining this to someone who has EXTREME difficulty with this stuff.

http://en.wikipedia.org/wiki/Hypotenuse

http://en.wikipedia.org/wiki/Sine_rule

Al.

sheeny (Al) · #19 28-05-2010, 08:17 PM

Quote:

Originally Posted by GeoffW1

Hyppopotamus with an education?

...and I thought it was a dangerous amphibious triangle...

Al.

Barrykgerdes · #20 28-05-2010, 08:30 PM

It is a pity that so few people understand mathmatics (particularly politititans)

The sine rule for solving triangles was one of the first things I learnt in trigonometry along with Pythagoras' theorem, and we had to prove the formulae were correct. However that was a long time before hand held scientific calculators.

Digital calculators were accounted for by five on each hand and only a small fraction of the class could use these accurately in any case but we at least had trig and log tables.

Barry