a circle has a radius of 9 inches. In inches, what is the length of the arc intercepted by central angle of 3.25 radians
1 answer:
Answer:
Step-by-step explanation:
Since we are given the central angle in radians, we should use the following formula for the arc length.
Where <em>s</em> is the arc length, θ is the angle in radians, and <em>r</em> is the radius.
We know this circle has a radius of 9 inches and the central angle is 3.25 radians.
- θ= 3.25
- r= 9 in
Substitute the values into the formula
Multiply.
The arc length is <u>29.25 inches. </u>
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Answer:
1.) ≈ 3.652
2.) I would say something about how the A in front of cos in the equation would change to 90, rather than stay 75 (in the equation for the step by step), but it would be easier to just use the Pythagorean theorem.
Step-by-step explanation:
I think we may have the same class so hopefully this helps:
1.) --> law of cosines formula.
--> plugged in numbers; when you draw the triangle, the included angle would be A, and the opposite side would be a. B and b, and C and c are opposite each other. In this case, a is the hypotenuse.
--> in between steps.
--> more simplifying.
--> answer
2.) This one is just an explanation: The 75 in the equation is the given angle, which is a. If this changes, it would just change in the equation too. And obviously, if it's 90 degrees, you can just use Pythagorean theorem a^2+b^2=c^2.
Good luck! :)