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I have a problem concerning radians and angles

It says calculate in degrees, the angle subtended at the centre of a circleof radius 2.7 cm by anarc of length 6.9 cm

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First of all you must realize that on a circle of fixed radius, the length of an arc is proportional to the angle that subtends it.
For example, to a 90 degree angle corresponds 1/4 of a circumference, to 180 degrees 1/2 the circumference. Double the angle, double the arc length.
Once this is understood you can say that
arc length = k*angle where k is the constant of proportionality or
l=k*a or k=l/a
Similarly
2*Pi*R=k*360 degrees or k=(2PiR)/360
It is the same k for the same circle
So
k=l/a=(2Pi*R)/360

You have a proportion l/a=(2Pi*R) /360
Knowing l an R you can isolate a

a= (180/Pi)*(l/R)
Your angle is
a=(180/Pi)*(6.9/2.7)=146.42 degrees
Now, you should note that the ratio 180 deg/Pi=57.29 is the value in degrees of an angle of 1 radian.

Posted on Oct 22, 2013

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About 146 and a half degrees.

If this is homework, be sure to show your work.

Posted on Oct 22, 2013

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SOURCE: finding the length of a triangle

might try

(54tan)/45

I don't have a calc that will do it or I would try it and see.

Posted on Aug 01, 2008

Elessaelle
  • 122 Answers

SOURCE: given a length of 30 cm on the x axis and a length

Yes, there is shortcut because this is right triangle, so you can use Pythagorean theorem (see picture).

  1. Length of hypotenuse is square root of sum of squares of lengths of other two sides of triangle, which is equal to square root of 30^2+10^2=31.6 cm.
  2. Sin(a)=longer cathetus/hypotenuse=0.949 so a=arcsin(0.949)=71.6 degrees
  3. Finally b=90-a=18.4 degrees.
elessaelle.png

If this was helpful please rate 4 thumbs :)

Posted on Sep 05, 2011

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SOURCE: Error when using inverse trig inever used to get

If you are trying to calculate arcsine (sin^-1) and arccosine (cos^-1) the only whole number you can use are -1,0 and 1. This due to the fact that the domain of these functions is the closed interval [-1,1]. Any value outside that interval will trigger an error message. No limitation on the argument of the arc tangent or arc cotangent functions

If the angle unit is set to degree the arc will be in degrees, and if angle unit is radian, the arc will be in radians.

Posted on Sep 29, 2011

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1 Answer

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There is probably a formula for this or other ways of doing this, but I will give it a shot.

An octagon has 8 sides (octopus has 8 legs). To make an octagon, we effectively have 8 triangles joined at the centre. In the centre, we have 8 equal angles. Since a full circle is 360 degrees, each of these angles must be 360 / 8 or 45 degrees.

Now we can just focus on one of these triangles. We have an angle of 45 degrees at the centre and two arms extending out 10 feet.

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Assume the central angle is 35 degrees and the radius is 1.

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Yes, there is shortcut because this is right triangle, so you can use Pythagorean theorem (see picture).
  1. Length of hypotenuse is square root of sum of squares of lengths of other two sides of triangle, which is equal to square root of 30^2+10^2=31.6 cm.
  2. Sin(a)=longer cathetus/hypotenuse=0.949 so a=arcsin(0.949)=71.6 degrees
  3. Finally b=90-a=18.4 degrees.
elessaelle.png

If this was helpful please rate 4 thumbs :)

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