angle APB=25  angle CPB=93  What is the measurment of arc AB?
437123
Looks like you're missing a few things here.  To find an arc length, you need a radius along with the measurements you gave.  If you had a length of one of the sides, say AP, then you could find the arc length by taking a ratio of that length compared to the circumference of a circle:\n\narc length / circumference = angle / 360\n\nIf you solve for the arc length and plug in your known values, you'd have\n\narc length = 2*pi*AB * 25 / 360\n\nFrom this, you can see that angle CPB is irrelevant.\n\nAlso, it's not clear that this is a circle.  You list two angles, and the only thing we can figure is that they both share a vertex at P.  It's not clear if A is between B and C or outside of it.  But again, it doesn't really matter how angle CPB plays into this, since the arc length is really a function of the angle it contains and the radius of the circle.
932598
The exterior angle is equal to the sum of the two interior angles.  So 18+98=116, your answer should be 116.  I'm assuming that the exterior angle is supplementary to angle 3, not angle 1 or 2.
884011
The sum of the measures of the EXTERIOR angles is always 360.  So subtract 162 from 180 to get an exterior angle (18) then divide 360 by 18 to see how many sides.
746093
It's straight ahead geometry.\nDraw a circle with center O.  Draw a diameter horizontally through the circle. Label the left intersect as A and the right intersect as B.  Now draw a vector from O to a point P on the circle.  What tdo you know about triangles AOP and BOP in terms of the angle the vector makes with the diameter?  Use law of sines, law of cosines, trig, etc. to show that angle APO and angle BPO add up to 90 degrees and your done.\n\n\nDoug
1030265
a=c*sin(30)=.5c since it is apposite the 30 degree angle\nb=sqrt(c^2-a^2)= .866c\nor b=c*cos(30)=.866c\n\na=b=c*sin(45)=.707c=
1092151
You'll have to give us a better idea of what you're trying to do.  An angular error of 1 second of arc corresponds to a deflection of 5 microns over a length of one metre.  It's difficult just making things smooth to 5 microns in a workshop, so any angle you measure will probably have an error in excess of 1 second anyway.\n\nI doubt any solution we can provide would fall under most definitions of "cheap".
623818
We can find angle B by subtracting the others from 180:\n\nB = 180 - 32 - 44\n= 104\n\nThe length of the sides can be found using the law of sines:\n\n(sin A)/a = (sin B)/b = (sin C)/c\n\nSo,\n\n(sin B)/b = (sin C)/c\n(sin 104)/b = (sin 44)/20\nb = 20(sin 104)/(sin 44)\n~ 27.94\n\n(sin A)/a = (sin C)/c\n(sin 32)/a = (sin 44)/20\na = 20(sin 32)/(sin 44)\n~ 15.26
966696
Arc=r.theta=8*pi/8=pi
763047
Angle 2*pi is one revolution, so this arc is the circumference!\n2*pi*radius = 18*pi\n\nThere is also the general formula \narc length = radius * angle (in radians), which of course gives exactly the same result here.  But after 2 hours I guess you're not there to see this answer!  Sorry no-one responded earlier.
749836
The 14 foot line is called a secant.  Bisect it, and draw a radius through the point of bisection.  You now have two identical right triangles, with hypotenuses of 12 feet, and known sides of 7 feet.  Use trigonometry to calculate the angle at the center of the circle of either triangle, and then a simple proportion (involving the circle's total circumference) will give you the arc length you want.
865942
b = 70sin55\n\nb = 57.34
618692
the correct option is e \n the value of i radian is 180/pi = 57.3248 ( if pi is 3.14)
343495
To find arc length, you need the angle that the arc subtends and the radius of the circle.  To find the angle, you'd have to do some geometry...\n\nImagine a triangle with sides 10, 10, and 5.  This is pretty much a chord on your circle (5) and the radii from the center to the ends of the chord (10).  If you draw a line from the center perpendicular to the chord, it bisects the chord.  This gives you two right triangles, with hypotenuse 10, side 2.5 (half the chord), and side unknown (the segment from the center to the chord).  To find the angle at the center formed by the radius and the unknown, you can use the sine function:\n\nangle = arcsin(opposite/hypotenuse)\nangle = arcsin(2.5/10)\nangle = 14.48 degrees or 0.25 radians\n\nThe total angle is then 0.5 radians, since the above only found half of that total angle.\n\nThe formula for arc length is\n\narc length = radius * angle\n= 10 cm * 0.5 rad\n= 5 cm\n\nAnd this kinda makes sense - if the total circumference is 20pi, and the arc is 28.96 degrees, then the arc length can also be found by\n\narc length = angle * circumference/360\n= 28.96 * 20pi/360\n= 5 cm
450833
join the 2 pointz frm da arc vit da radius.measure out da value of da angle forned here.then substitute da values 4 this formula:  2*pie*radius/da angle u measured\n\nhappy solvin!
951198
^ Parasite alert LOL! ^\n\n30 s for C to move from A to B, maybe? I'll assume that. Also, x seems to be a length, not an angle. Maybe a) is asking for the rate of change of z (called z')? We know the angular rate of C about O (y') is pi/30 (answer to b)), and triangle CAO is isosceles, so z'=-0.5*pi/30. \nFor c), circumferential velocity is pi*r/30. Angle CAO is, conveniently, 45 deg, so x' = sqrt(0.5)*circumferential velocity.\nFor d), the area of triangle OAC is .5*AO*altitude, and altitude=r*sin(y). This is a maximum when y (not x) =pi/2.\nSorry, I know you wanted  no answers, but I couldn't see how/where to stop short of most of the answers.
708770
angle cdb = ancle cbd   (since traingle cbd is an isosceles)\n\nangle bcd =  180  -  (2*65)   =   50\n\nangle  acb =   180 - 68 - 30 =  82\n\n\n\nUsing sine rule,  (considering traingle  abc)\n\n(ab/sin 82) =  (bc / sin 68)\n\ngiven: ab= 5  ,  therefore  bc = 4.68   (2 decimal places)\n\n\n\n\nusing sine rule again,   (for triangle bcd)\n\n(bd/sin 50) =  (bc / sin 65)\n\nbc= 4.68   ,  therefore  bd = 3.96
801229
90° < beta < 180° means 2nd quadrant.\nsin beta = 12/13 \nbeta=arcsine(12/13)=67.38° in the 1st quadrant\nor 180°-67.38°=112.62° in the 2nd.\n\ntan beta = 3/4 , sin beta < 0\nsin beta<0 means 3rd or 4th quadrant.\ntan beta>0 means 1st or 3rs quadrant so we are in the 3rd quadrant.\nbeta=arctan 3/4=36.87° in the 1st quadrant. or\n36.87°+180°=216.87° in the 3rd.