Question

Find the angle theta in radians.
( PLEASE SHOW STEPS )

Answer 1

if you notice, the radius of the circle is 5, and the arc made by θ is 15 units long.


`\bf \textit{arc's length}\\\\ s=r\theta ~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\ ------\\ r=5\\ s=15 \end{cases}\implies 15=5\theta \implies \cfrac{15}{5}=\theta \implies \stackrel{radians}{3}=\theta`

Answer 2

Hello!

As you can see, we have a radius of 6. If we divide, this means that this is 2.5 radians. To convert radians to degrees we use the formula below.


`(180)/( \pi )x`

First of all we divide 180 by pi.

180/
`\pi`≈57.3

Now we multiply by 2.5

57.3(2.5)=143.25°

Note that the angle we see is obtuse, or greater than 90°.

Therefore, ∠θ≈143.25°

Now we need to convert this back into radians. This can be represented by the equation below.


`( \pi )/(180)x`

First we divide pi by 180 then multiply by our angle.


`\pi`/180(143.25)≈2.5

Therefore, our angle theta is about 2.5 radians.

I hope this helps!