In a large city, commuter trains are used to transport people into the downtown area. Trains arrive many times a day to a downtown station. While most are on time, some are late. The table shows on-time data from the past week. Train Status
On Time Late Total
Day of the Week Monday 32 8 40
Tuesday 24 16 40
Wednesday 37 3 40
Thursday 29 11 40
Friday 30 20 50
Total 152 58 210
What proportion of trains were late on Tuesday?

StartFraction 8 Over 40 EndFraction
StartFraction 58 Over 210 EndFraction
StartFraction 16 Over 40 EndFraction
StartFraction 24 Over 40 EndFraction

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

step-by-step explanation:

hihi so drawing these 2 triangles is fairly simple. all that's left is finding the height of each one. luckily, we have a side length and an angle, so there is a trig function we can use to solve for the height. the easiest one to use would be tangent, since we have 2/3 things needed to find and the third needed is what we are solving for. tan(73°) * 30 ~= 98.13 and tan(73°) * 35 ~= 114.45