Question

sprinkler rotates back and forth from point A to point B. The water reaches 8 meters from the base of the sprinkler. What is the length of Arc capital a capital B, rounded to the nearest tenth of a meter? Use 3.14 for pi

Answer 1

We have the following general rule for the arc length:

`\text{arc length =}(2\cdot\pi\cdot r\cdot\alpha)/(360)`

where r is the radius and alpha is the angle.

In this case, we have the following information:

`\begin{gathered} \alpha=150\degree \\ r=8 \\ \pi=3.14 \end{gathered}`

then, using the formula, we get:

`ArcLength=(2\cdot(3.14)\cdot(8)\cdot(150))/(360)=(7536)/(360)=20.9`

therefore, the arc length is 20.9m