Question

The circumference of the circle is 160 mm. a) if the length of arc AB when <1= 40.05°b) <1 when are AB = 35.62 mm

Answer 1

Given an arc with length l of a circle with circumference c such that the arc subtends an angle of

`\theta`

then we must have that

`l=(\theta)/(360^0)* c`

In this case,

Therefore,

b)

In this case,

`\begin{gathered} 35.62=(\theta)/(360^0)*160 \\ \\ \text{this implies that} \\ (35.62)/(1)=(160\theta)/(360^0) \\ \text{ Cross-multiplying, we have} \\ 160\theta=360^0*35.62 \\ \text{therefore} \\ \theta=(360^0*35.62)/(160)=80.15^0 \end{gathered}`

Therefore ,

<1 = 80.15 degrees