
Dec 12th, 2002, 05:02 PM
#1
Thread Starter
PowerPoster

Dec 12th, 2002, 06:37 PM
#2
Member
posted it in galah but its 240

Dec 12th, 2002, 07:07 PM
#3
Thread Starter
PowerPoster
that's good thanks but how did you get that...i need to be able to do it for any length of sides

Dec 12th, 2002, 10:41 PM
#4
Fanatic Member
write the black line as x, so the green line is (500x). let the red line be k. set up two pythagorus equations. solve for x. then solve for k.
Massey RuleZ! ^^__ Cheers! __^^ Massey RuleZ!
Did you know that...
The probability that a random rational number has an even denominator is 1/3 (Salamin and Gosper 1972)? This result is independently verified by me (2002)!

Dec 13th, 2002, 04:50 AM
#5
Fanatic Member
right angled
Another possible way using areas:
1) Work out the angle opposite the side 300 (use cosine rule)
2) Work out the area using this angle and the sine rule
3) Divid the area by 2, then by 500, and you get the height
i.e. cos (A) = (400^2 + 500^2  300^2)/(2*400*500)
=> work out A
=> know sin(A) = (1 cos(A)^2) ^ 1/2
=> know area = 1/2 * 400 * 500 * sin(A)
=> know height = area/(2*500)
=> work out green line using cosine rule in 400red linegreen line triangle
=> work out black line = 500green line
sql_lall

Dec 13th, 2002, 05:51 AM
#6
Addicted Member
The entire triangle must be right angled, because it obeys pythagoras theorem.
Try two simultaneous equations with the sine rule (calling the red line R):
Call black line X and red line R, angles in degrees for ease of use:
sin60 / R = sin30 / X
X/2 = R(Root3/2)
X = R(Root3)
sin30 / R = sin60 / (500  X)
Sticking in for X, that gets you:
1 / 2R = (Root3/2) / (500  R(Root3))
So R = 250 / Root3 = 144.33756729740644112728719512549...
Now that's assuming those angles are what I educatedly guessed them to be. I mean it all looks nice and neat that way.
Not at all related to sheep...

Dec 13th, 2002, 05:52 AM
#7
Addicted Member
And for my next amazing feat of genius, I will disappear from these forums for an entire week because I'm going skiing in France! Cyas!
Not at all related to sheep...

Dec 13th, 2002, 05:33 PM
#8
Addicted Member
Use Heron's Formula; it has never failed since I used it to solve the first difficult geometry problem that I could do.

Dec 13th, 2002, 05:56 PM
#9
Fanatic Member
with Assbandit noticing that A+B=90, and you know the side lengths, use the law of tangents!
Massey RuleZ! ^^__ Cheers! __^^ Massey RuleZ!
Did you know that...
The probability that a random rational number has an even denominator is 1/3 (Salamin and Gosper 1972)? This result is independently verified by me (2002)!

Dec 13th, 2002, 11:52 PM
#10
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