1) what angle pheta is measured by a 7inch arc on a circle of radius=3
Find: Radians=
Degrees=
revs=

2) if the 8inch radius tires on a car are rotating at 600revs per minute, how fast is car going mph ?


3) assume the earth orbits the sun once per year (365 days), in a circular way with sun at the center, also earth is 93,000,000 miles from the sun. what is the linear speed of the earth in miles per hour??


4) in right triangle, an acute angle and its adjacent side measure 40degrees and 15 feet respectively. draw a diagram to detemrine the measures of the other side, hypotenuse, and other acute angle.




5) if a mechanical horse is moving around a circlular track with radius 200 yards at 20mph, how many revolutions per day does the horse make?



Thanks in advance

Ok, first off, its "theta" not "pheta," i don't really mind misspellings, as long as you can get what the person is trying to say, but apparently a lot of people here do, see Spelling

Ok, the formula for length of arc in radians is:
s = r@

where s is the arc length, r is the radius, and @ is supposed to be the symbol theta, which is measured in radians.

the formula for arc length in degrees is
s = @/360 * 2pi*r

we won't need both formulas, one is enough. let's use the radian formula since its simpler.

s = r@
=> @ = s/r
if s=7, r = 3
@ = 7/3 radians

now to convert from radians to degrees, we multiply by 180/pi
so @ = 7/3 * 180/pi = 420/pi degrees

but how many did we make? we can use either the radians or degrees to find out

Using degrees, Revs = (420/pi)/360 = 7/6pi revs = 0.371 revs

or

Using radians, Revs = (7/3)/2pi = 7/6pi revs = 0.371 revs

what is the circumference of the tire?

C = 2pi*r = 2pi(8) = 16pi inches. or 50.265 inches

it makes 600 revs per minute, so the distance traveled in one minute is 600*C = 9600 inches per minute
but one minute is 1/60 th of an hour. so the distance travelled per hour is:
60*9600 in/h = 576000 inches per hour

now we have to convert inches to miles, i don't know that off the top of my head, so let me consult the all-knowing Google....

And the Google says: 1 inch = 1.57828283 x 10^-5 miles

so the car travels at 576000(1.57828283 x 10^-5) mph = 9.09 mph

Speed = distance/time

what is the distance the earth has to travel? Well, that's just the circumference of its circular path of orbit, and what's that?

C = 2pi*r = 2pi*93000000 = 186000000pi miles.

what is the time it takes?
Didn't you read the question! It takes 365 days
I know that silly, but we need time in hours!
Fine! Don't shout at me! The time in hours is:
365*24 = 8760 hours

Thus, speed = 186000000pi miles/8760 hour = 21232.88pi mph

Ok, i drew a diagram like you told me to, now what?
Now we find what they asked us to find...duh
easier said than done, as is anything in life--except watching tv

let the hypotenuse be a, the opposite side be b and the unknown angle be x (see diagram below)

Let's find the hypotenuse first.

cos(40) = 15/a
=> a = 15/cos(40) = 19.581

now we know two sides. we can use trig rations to find the other side, or pythagoreans theorem. let's keep practicing our trig ratios (warning, i rounded off decimal places, so the answers are not exact)

tan(40) = b/15
=> b = 15tan(40) = 12.586

for the other angle, angles in a triangle add up to 180

so x = 180 - (40 + 90) = 50

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Hello, Stuck686!

Sounds like you need lessons on converting units . . .


The circumference of a circle is: .C .= .2πR . (R = radius)

The radius of Earth's circular orbit is: .R = 93,000,000 miles.

The length of Earth's orbit is: .C .= .2π(93,000,000) .≈ .584,336,234 miles

Hence, the Earth travels 584,336,234 miles in one year.


584,336,234 miles . . . .1 year . . . . .1 day
---------------------- .x .----------- .x .----------- . ≈ . 66,705 miles/hour
. . . . 1 year . . . . . . . 365 days . . .24 hours

how many yards are in a mile? again we consult google, we find:
1 mile = 1760 yards

so the horse travels at 20(1760) yards per hour = 35200 yards per hour

that is 35200(24) yards per day = 844800 yards per day


now what is the circumference of the track?

C = 2pi*r = 2pi*200 = 400 pi yards

so revs in one day = 844800/400pi revs = 2112/pi revs

Ok, Stuck686, before you go, that's different from what Jhevon got, notice that my answer had pi in it, it is the same when you work it out. that being said, notice that several of my answers have pi in them, that's because i wanted to cut down on rounding of decimals, so the answer is more exact

wow awesome guys thanks so much for the help