GoldenLeaf

Ah, lovely, an easy one. Equilateral triangle. After this one I'm eating dinner x3

60 - 60 - 60 means all sides are equal. Altitude splits this one perfectly in half as well, and makes a 30 - 60 - 90 triangle. 30 - 60 - 90 means x - x(squareroot(3)) - 2x.

2x is equal to one of the original legs, which is 18. x is equal to the split leg, or 9. x(squareroot(3)) equals the altitude, and since x = 9, x(squareroot(3)) = 9(squareroot(3))

9(squareroot(3)) is your answer.

It's the altitude, right?

If I recall correctly (haven't had school for a month, Geometry in longer, so forgive me) the altitude is the line at a direct right angle from a side?

The altitude in this case would be against the hypotenuse.

SO, for this, the legs for this side are 6 and 6. This makes it a 45 - 45 - 90 triangle, which brings up something cool: we already know the length of the hypotenuse. 45 - 45 - 90 = x - x - x*squareroot(2) Therefore, the length of the hypotenuse is 6squareroot(2)

This brings another funny fact: the altitude, because it is an isoceles right triangle, perfectly splits the hypotenuse in half. In this case, the "squareroot(2)" acts as a variable (6/2=3) and does not affect the 6 or 3.

This brings up yet another sweet thing: It just made another isoceles right triangle, except instead of the legs being 6 and 6, the legs are 3squareroot(2). The altitude is one of the legs now, and thus the altitude's length is 3squareroot(2).

Oh, and Zegroes, you're probably older than me, so you have NO RIGHT.

272500/381500

Well, you can take 100 from each side right off the bat.

2725/3815

Take it by 5

(2725/5)/(3815/5) = 545/763

From here, notice the 45 and 63? They are both divisible by 9, and the numbers in fromt of 45 and 63 (5 and 7, respectively) are the numbers multiplied by 9 to get the 45 and 63

EX:

5 45

5 * 9 = 45

7 63

7 * 9 = 63

You can divide each side by 109

(545/109)/(763/109) = 5/7

Final ration = 5/7

2.5 = 2 1/2

1/2 = 4/8

2 = 16/8

(16+4)/8 = 20/8

20/8 = 24 miles per 1/8 th of a mile

20 eighths

20*24 = 480

The two cities are 480 miles apart

Do an inverse cosine function.

cos x = 0.08696 goes to (acos(0.08696))= x

Plug (acos(0.08696))^-1 into a calculator

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}^{\!\!\mathtt{-1}}{\left({\mathtt{0.086\: \!96}}\right)} = {\mathtt{85.011\: \!257\: \!976\: \!987^{\circ}}}$$

x = 85.011 deg.

Shrek is the antithesis of love and life and anything mildly enjoyable.

In other words, no.

Well he's not online if that's what you're thinking XD

Well, I think we can beat the End of Day Wraps =)

Oooookaaaaaaay...

Yes Zeg, I see what I did here.  And you know my response?