Question

How do you find the radian measure of the central angle of a circle of radius $ 8 $ feet that intercepts an arc of length $ 14 $ feet?

Answer 1

Hint: Here we are given the intercept length and the radius, so using the correlation to find the angle in radians can be done by the standard formula $ \theta = \dfrac{s}{r} $ where $ \theta $ is the angle in radians, s is the intercepted arc and r is the radius of the circle.

Complete step-by-step answer:
Given,
s=14 and r=8
Now, take the standard formula,
 $ \theta = \dfrac{s}{r} $
Place the values in the above equation –
 $ \theta = \dfrac{{14}}{8} $
Find the factors in the above expression –
 $ \theta = \dfrac{{2 \times 7}}{{2 \times 4}} $
Common factors from the numerator and the denominator cancel each other. Therefore, remove from the numerator and the denominator.
 $ \theta = \dfrac{7}{4} $
This is the required solution.
So, the correct answer is “ $ \theta = \dfrac{7}{4} $ ”.

Note: Generally, the length of the straight sided shapes such as square, rectangle, triangles outlines is called its perimeter and the length of the circle’s outline or any arc’s such as semi-circle outline is called its circumference and $ \pi $ is used in the formula whereas perimeter is sum of all the sides using additions. The perimeter of a circle is also known as the circumference of the circle and it is the measurement of the boundary of the circle. Perimeter of the circle is $ = 2\pi R $ where; R is the radius of the circle. Alternative method to find the perimeter of the circle $ = \pi D $ , where D is the diameter of the circle.