Question

Given triangle(ABC) where A=(2,5), B=(-3,-1), and C=(-2,4). If d(A,B)=(61)^(1/2), d(A,C)=(17)^(1/2), and d(B,C)=(26)^(1/2) determine the area of tri. (ABC) using:
a. Area=1/2acsinβ
b. Area=1/2(base)(height)

NB: i tryed it and got a beta but i think its wrong and i can't figure how to get the height

Answer 1

you already have the angle.....I can show you have to do this in twiddla

Answer 2

whats twiddla?

Answer 3

http://www.twiddla.com/solved

Answer 4

distance from B to A is
\[\sqrt{61}\] and distance from B to C is
\[\sqrt{26}\] so now all you need is the angle at B.

Answer 5

for this i think you are going to have to use the law of cosines

Answer 6

\[\cos(B)=\frac{a^2+c^2-b^2}{2ac}\] where a, b, c represent the lengths of the side opposite the angles A, B, C

Answer 7

\[a=\overline{BC}=\sqrt{26}\]
\[c=\overline{AB}=\sqrt{61}\]
\[b=\overline{AC}=\sqrt{17}\]

Answer 8

this problem is a pain

Answer 9

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Answer 10

sensei do you have a better idea? ok quit fooling around!

Answer 11

oh that is actually the picture! nice

Answer 12

its the 3 points of the triangle :)

Answer 13

i am still trying to find angle B

Answer 14

\[\cos(B)=\frac{26+61-17}{2\sqrt{26}\sqrt{61}}\]

Answer 15

angle can be found with vectors right?

cos(a) = a.b/(|a| |b|)

Answer 16

probably easier. i was using law of cosines, which is of course the same thing. go getem.

Answer 17

i get B = 28.5 degrees. so the area is
\[\frac{1}{2}\sqrt{26}\sqrt{61}\sin(28.5)\]

Answer 18

and that was a royal pain.

Answer 19

by my calculation area is 9.2

Answer 20

computer dumped n me

Answer 21

i meant 9.5 dumped me too

Answer 22

A=(2+3,5+1), B=(-3+3,-1+1), and C=(-2+3,4+1).

A=(5,6), B=(0,0), and C=(1,5)

d(A,B)=sqrt(61)
d(A,C)=sqrt(17)
d(B,C)=sqrt(26)

a.c=
<5,6>
<1,5>
-------
5+30 = 31

cos(B) = 31/sqrt(61*27) right?

Answer 23

dot i can do ...adding? nah!! lol

Answer 24

hmmm i got 35 in my numerator but i could certainly be wrong

Answer 25

same denominator though

Answer 26

5 + 30 = 35 :)

Answer 27

whew. vectors easier than law of cosines, although they really are the same.

Answer 28

oh right! 5 + 30...

Answer 29

A=(5,6), B=(0,0), and C=(1,5)

a-c =

<5,6>
-<1,5>
-------
<4,1>

-a<-4,-1>
-ac<-5,-6>
---------
20+6 = 26

cos(A) = 26/sqrt(61*17) right?

Answer 30

think it is time for me to retire. maybe smoke some sensei and go to bed

Answer 31

C = -c.ac

<-1,-5>
< 4, 1 >
---------
-4 -5 = -9

cos(C) = -9/sqrt(17*27) maybe?

Answer 32

maybe wanna make the 9 lol