Question

What will be the length of \[x\] and \[y\] if there is a circle, \[x\] is the arc length, there is an angle of \[120\] degrees and \[y\] is the hypotenuse?

Answer 1

Hint: The above problem is based on the concept to find arc length of a circle. So here we need to convert \[120\] degrees to a radian measure which is \[2\pi = 360\] degree and in the formula \[x = aR\] substitute it. In this formula mentioned \[x\] stands for length of an arc and we need to perform required calculations and find the value of \[x\] in cm and with correlation we can find \[y\]

Formula used:
In order for solving the above question the formula used is
\[x = aR\]
Where \[x\] is the arc length, \[R\] is the radius and \[a\] is the central angle

Complete step by step solution:
In the question asked we are asked to find the length of an arc of circle of radius \[12\] cm which subtends an angle of \[120\] degrees
We will use formula
\[x = aR\]
This gives
\[x = 120y\]

So in this case arc length is \[x = 120y\]

Note: A portion of circumference of circle is an arc and the length of an arc is basically length of its portion of circumference.
Keep in mind that arc length is a fractional part of the circumference. While solving such types of problems try making the required calculations in the equation for getting a final solution. Remember not to make any calculation mistakes due to sign conventions and converting degree into radians. We can also solve \[x\] without the use of formula in alternate way
Since \[{360^ \circ } - - \rangle \] full perimeter\[2\pi y\], or \[360y\]
\[{1^ \circ } - - \rangle \]arc length= \[\dfrac{{360y}}{{360}}\]
Which means \[{120^ \circ } - - \rangle \]arc length will be
\[x = \dfrac{{(360y)(120)}}{{360}} = 120y\]