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finlep [7]
3 years ago
6

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

Mathematics
2 answers:
Kisachek [45]3 years ago
8 0
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
yKpoI14uk [10]3 years ago
3 0
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.

\frac{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, ∠<span>θ</span>≈143.25°

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

\frac{ \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!
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