autox
[Top] [All Lists]

RE: Math problem (triangle area solution)

To: "Matt Murray" <mattm@optonline.net>, <general@rennlist.org>,
Subject: RE: Math problem (triangle area solution)
From: "Adamson, Ken" <KADAMSON@lifeline.net>
Date: Wed, 5 Nov 2003 11:15:25 -0600
-----Original Message-----
From: owner-autox@autox.team.net [mailto:owner-autox@autox.team.net]On
Behalf Of Matt Murray
Sent: Wednesday, November 05, 2003 9:30 AM
To: general@rennlist.org; autox@autox.team.net;
evolution-discussions@yahoogroups.com; nersolo@ner.org
Subject: Math problem (triangle area solution)


Okay, we know I am a little thick.  :^)

I gotta triangle that one side is 190, the next side is 125 and the third 
is 170. How much area do I have?

I should know this but I am blanking out.

TYIA,


Matt Murray 


Ken Writes:

You probably aren't blanking out - it's hard.  Unless you use trig every day, 
you probably won't remember :)

If it's a right triangle, which it appears this is not, then your formula is 
one half the base times the height.
For oddball triangles, acute or obtuse - yours is acute, it's still one half 
the base times height, but you have to calculate what the base and height are, 
since they aren't given by the length of the sides.  You have to use some 
trig...

K = 1/2 abSinC

Enter the "Law of Cosines"
Angles opposite from a side have the same letter, only uppercase.
In my notation "c2" is "c squared"

For any triangle
Angles: A, B, C
Sides: a, b, c

Law of Cosines(three forms):
a2 = b2+c2-2bcCosA
b2 = a2+c2-2acCosB
c2 = a2+b2-2abCosC

In order to find the area, you have to drop a perpendicular from one of the 
points - visually, you usually try to lay the triangle down on its longest 
side, and drop a perpendicular from the opposite angle.  Once you do this, and 
figure out that angle, then you can use some pretty straightforward trig to 
find the area.

a = 125
b = 170
c = 190

Find the size of the largest angle first - this will be the one opposite the 
longest side (don't make me prove it...)

190*190 = 125*125+170*170 - 2*125*170*CosC      (substitute)

36100 = 15625 + 28900 - (10625 * CosC)          (do some math)

-8425 = -(10625 * CosC)                                 (do some algebra)

8425 = 10625 * CosC                                     (some more algebra)

CosC = 8425/10625                                               (take the 
inverse cosine)

C = 37.539 degress

Now we have an included angle, so we can switch to the area formula:

K = 1/2 * abSinC

K = .5 * 125 * 170 * Sin(37.539)

K = 6473.793 square units

Thus ends the trigonometry lesson...

Ken
'01 PT Cruiser Limited
HS101 in OKC (soon to be STS101)





<Prev in Thread] Current Thread [Next in Thread>