Please help me with these problems. I have a test tomorrow, I could REALLY use your help.?

Question

An equilateral triangle is inscribed in a circle of
radius r. Express the circumference, C, of the circle as a function of
the length, x, of a side of the triangle

I have NO idea on how to even approach this. The answer is supposed to be 2(pi)(x) radical (3) / 3

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Two cars leave an intersection at the same time.
One is headed south at a constant speed of 50
miles per hour. The other is headed east at a
constant speed of 120 miles per hour. Express
the distance, d, between the two cars as a
function of the time, t.

The answer is d(t) = 130t. How do I get that?

Gosh please help. You'll make my Night!!!!

Answer 1

a picture and explanation of the first problem is available at the following link

Answer 2

First draw an equilateral triangle, then draw a circle around it.
Now we know C=2Pi*r, but what is r in relation to x?
draw two radii that bisect two of the triangle's angles. you will have formed an isosceles triangle: two sides have length r, the other side has length x.

the largest angle of this isosceles triangle is 120 degrees (it's 1/3 of the circle). bisect this angle so you form two smaller triangles. both of these will be 30-60-90 triangles, from which we can immediately see:
cos 30 = (x/2)/r
solve for r:
r= x/sqrt(3) = sqrt(3) * x/3
now plug this into C=2*Pi*r
C=2*Pi*x*sqrt(3)/3

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draw a diagram!
you'll have a right triangle
now recall thatdistance is speed times time, so
one side has length x=(120mi/hr)t
other side has length y=(50mi/hr)t

distance between them is the length of the hypotenuse
use Pythagorean theorem
d = t*sqrt(120^2+50^2) = 130t

Answer 3

Equilateral triangle has all angles equal to 60º. The radii to the vertices form isoceles triangles with the duplicate angles equal to 30º, leaving the central angle at 120º. Drop an altitude from the center, which creates a 30-60-90 right triangle whose hypotenuse is the radius.

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Say the cars traveled 1 hr, you'd have what sides for the right triangle?

Answer 4

You're waiting until the NIGHT BEFORE the test to try and learn the answer?!!? You should watch some TV, then go to bed, then try and learn the answer when you're walking to class to take the test...