Question

Hello can you help me solve this trigonometry question and in the question use pi to answer it

Answer 1

The area A of a portion of a circle is:

`A=\pi\cdot r^2\cdot(\alpha)/(2\pi)`

Where alpha is the angle of the portion of the circle. So, to find the radius, we clear 'r' from the expression above:

`38=\pi\cdot r^2\cdot(1)/(2\pi)\cdot(7)/(5)\pi`

We can cancel the pi on the left of 'r' with the one on the right (the one that's dividing):

`38=r^2\cdot(7\pi)/(2\cdot5)`

So, now we clear 'r':

`(38\cdot2\cdot5)/(7\cdot\pi)=r^2`
`\sqrt[]{(380)/(7\pi)}=r`

So, the answer is:

`r=\sqrt[]{(380)/(7\pi)}km`