Sunday, November 14, 2010

Fox 314

Bleaug adds new meaning to "laziness". Hmmm, do your lazy tricks lazy scientists to solve this one, huh? Although not confirmed, the similarity of the terms with Fox 3 is striking. Enjoy...

1. In left white triangle:
x/sin(b)=a/sin(120)

In bottom white triangle:
x/sin(a)=b/sin(120)

then, multipliying:
x²=4*(a*b*sin(a)*sin(b))/3
Apply sin(a)=a/c and sin(b)=b/c (c=hypothenuse).

Venezuela

2. César's use of sin rule and pythagoras reveals the answer. There should be other approaches as well. Let's list the lazy observations for this case:

1. x=f(a,b) is formula-symmetric for a and b, due to rotation.

2. the unit of x is "length", in other words, units of a, b, and x are identical, as it should be.

3. a=0 or b=0 => x=0

4. x <= min{a,b}

3. Oh, one more thing: if one of the corners "must" always be on the right angle, then there should be further limitations on a,b,c right triangle. Even if that condition was removed, the formula for x will remain the same, won't it?

4. From the area of right triangle

(sqrt(a^2+b^2)*x*sqrt(3)/2)/2=a*b/2

5. Newzad yours looks like the easiest:

A(right triangle) / A(equilateral = hypotenuses / x
(Because their heights are equal)

=> [ab/2] / [x^2 sqrt(3)/4] = sqrt(a^2 + b^2)/x