Hey, I'll quote the problem: "In the US, circular railroad curves are designated by the degree of curvature, the central angle subtended by a chord of 100 ft. Suppose a portion of track has curvature 42 degrees.
a) What is the radius of the curve?
b) What is the length of the arc determined by the 100 ft chord?
c) What is the area of the segment of the circle bounded by the arc and the 100 ft chord?

i dont have time to work it out.

But u should get an F for a terrible ms paint diagram :em321:

if(getThingFlags(source) & 0x8){
  do her}
elseif(getThingFlags(source) & 0x4){
  do other babe}
else{
  do a dude}

I got your radius. Don't have time to try and remember the rest. Better drawing too.

Well, I'm not sure what you were doing there, but the answers in the back of the book are:

a) ~140 ft
b) ~102 ft
c) 622 sq ft

Any ideas?

Yoshi did his math wrong...

180-42=138
138/2=69 (Measurement of the other two angles in the triangle)

42/100=69/r
42*r=100*69 (cross multiplying)
r=6900/42
r=~164.29

Hm... I did the math right, but it's wrong with the answer from the book. Maybe we're doing it the wrong way. It's been too long since I took trig/geo.

Well I think it involves one of the trig functions but I'm not sure.

You can find x by taking the sin of 42 times 100. (Sin = Opp/Hyp) and the other side of that triangle by taking the cos(42)*100. (Cos is Adj/Hyp. The old saying is Soh Cah Toa. Sin = opp/hyp, Cos = adj/hyp, tan=opp/adj)

The cos will also give you the radius of the circle (Which is also x. Actually, x and the other side should be the same.)

Edit- Right! I forgot to explain something. You have to rearrange the sin = Opp/Hyp equation. You know the sin angle, and you know the opposite, so you can make the equation: opp*sin(angle) = hyp

That only works for right triangles.

I found it! Law of Sines!

sin(A)/a = sin(B)/b = sin(C)/c

100 / $sin(.73037) = x / $sin(1.204277)
100 / 0.667145 = x / 0.93358
139.936595 = x

(angle measurements are in radians... I was using mirc for math)

Which isn't working out.

(I'm doing it with him)

I figured it out! I'm just letting Vinny post it.

hurrah for ISOSCELES triangles

So, to the find the radius, you use the law of sines:

a/sin(A) = b/sin(B)

For this problem,

a=100
A=42°
b=r
B=69°

So, using the law of sines, you get

100/sin(42°) = r/sin(69°)
sin(69°) * 100/sin(42°) = r
r = ~139.94



Then, to find the length of the arc, you multiply the circumference of the entire circle by the percentage of the circle the arc makes up. So,

length of arc = 42°/360° * (2*pi*r)
l = 0.116667 * (2 * pi * 139.94)
l = 0.116667 * 879.268952
l = ~102.58



Lastly, to find the area bounded by the arc and the chord, you would find the area of that slice of the circle, and subtract the area of the triangle.

First, the area of the slice would be...

S = 42°/360° * (pi*139.94^2)
S = 0.116667 * 61522.448564
S = 7177.639507

The area of the triangle is... (I'm not sure about this, part. I forgot the formula for area of a triangle, so this is from some website)

Area = a*b*sin(C)/2
T = 100*139.94*sin(69°)/2
T = 6532.25926

So...

7177.639507 - 6532.25926
~645.38



That last number is a bit off... but I think I did pretty good for someone who hasn't done this in 3 years and is using a chat program as a calculator. Hopefully this'll make sense to you...

ty, yeah 645 is close for me.