-----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)
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