Answer :
Answer:
is 171.8 degrees
Step-by-step explanation:
Length of arc subtended by any angle [tex]\alpha[/tex] with a radius r is given by [tex]\alpha *r[/tex].
For example
to calculate length of circumference
angle subtended by whole circle is 2[tex]\pi[/tex]
Therefore length of circumference is [tex]2\pi *r[/tex]
Similarly we can see that for semicircle angle at center is [tex]\pi[/tex]
hence length of arc is [tex]\pi r[/tex]
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Given in the problem length of arc = 3r
radius= r
let the value of angle be [tex]\alpha[/tex]
Plug in the value of length of arc in formula to calculate length of arc we have
3r = [tex]\alpha* r[/tex]
[tex]\alpha[/tex] = 3r/r = 3
This value of angle subtended is in radian, we need to convert radian into degrees.
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We know that [tex]\pi[/tex] is equivalent to 180 degrees.
Also value of [tex]\pi[/tex] is 3.14
hence 3.14 radian= 180 degrees
=>3.14/3.14 = 180/3.14 ----degrees dividing both side with 3.14
=> 1 radian = 57.325 degrees
=> 1*3 radian = 57.325 * 3 degrees( multiplying both side with 3 as we need to find value of 3 radian into degrees
=> 3 radian = 171.8 degrees.
the measurement of the angle that subtended by the arc is 171.8 degrees or in radian 3 radian
