$Need formula help$

Question

$Need formula help$

An engineer is asked to design a water sprinkler that will cover a field of 75 square yards that is in the shape of a sector of a circle of radius 12 yards. Through what angle should the sprinkler rotate?

Can somebody help me with the formula for this?

Trigonometry

Chelsrenee

11

Report

Answer

The answer is accepted.

Join Matchmaticians Affiliate Marketing Program to earn up to a 50% commission on every question that your affiliated users ask or answer.

Answer 1

Answers can only be viewed under the following conditions:

The questioner was satisfied with and accepted the answer, or
The answer was evaluated as being 100% correct by the judge.

View the answer

The area of a circular sector with radius $r$ and angle $\theta$ (in radians) is
\[A=\frac{r^2 \theta}{2}.\]
In the given exaample we have $r=12$ and $A=75$. Substituting in the above formula we get
\[75=\frac{12^2 \theta}{2}=\frac{144 \theta}{2}=72\theta.\]
Hence
\[\theta =\frac{75}{72} \text{radians}.\]
If you want the angle in degrees then it is
\[\frac{75}{72} \times \frac{180}{\pi}=60.523 \text{degrees}.\]

Erdos

4.7K

Erdos

0

Leave a comment if you need any clarifications.

$Need formula help$

Answer

Related Questions

Search