Question

An architect is sketching a doorway, the top of which is part of a circle of a radius 50 in. The central angle is 100

Answer 1

How many inches long will the arc be?

Answer 2

\(\bf \textit{arc length}=s=\cfrac{\theta \pi r}{180}
\\ \quad \\
r = radius\qquad \theta=\textit{angle in degrees}\)

Answer 3

How would you set it up i am confused

Answer 4

well, what's the given radius?
what's the given angle?

plug them in

Answer 5

\(\bf \textit{arc length}=s=\cfrac{\theta \pi r}{180}
\\ \quad \\
r = radius=50\qquad \theta=\textit{angle in degrees}=100
\\ \quad \\
\textit{arc length}=s=\cfrac{100\cdot \pi \cdot 50}{180}\)

Answer 6

An architect is sketching a doorway, the top of which is part of a circle of a radius 50 in. The central angle is 100 ... 100 what? If you have that unit of measurement correct, then JDoe's suggestion would make more sense.

Answer 7

the general formula for arc length is very simple: s = r*theta, where theta is the central angle. theta must, repeat, must, be in radians.

Answer 8

radius is 50
given angle100

Answer 9

I do not understand could you set it up please?

Answer 10

ok so 100*3.14*50/180=87.2
The answers are \[43\left(\begin{matrix}41 \\ 63\end{matrix}\right)\]
\[87\left(\begin{matrix}19 \\ 63\end{matrix}\right)\]
\[130\left(\begin{matrix}60 \\ 63\end{matrix}\right)\]
164\[164\left(\begin{matrix}38 \\ 63\end{matrix}\right)\]

Answer 11

s = arc length = (radius) * (central angle, in radians)

What is the radius? You'll need to write more than just '50'.

what is the central angle? You'll need to write more than just '100.'

Answer 12

In other words: Please always include units of measurement when talking about some measure.

Answer 13

The only measurement the give me is inches

Answer 14

Yes. So then please type in "50 inches" for the radius, not just '50.'
I'd bet that if you go back and look at the original problem, you'd see that the central angle is 100 degrees. Why? because 100 radians would be about 5,730 degrees. I'm sure you haven't ever heard of a central angle of 5,730 degrees.
So, please type in "100 degrees" for the central angle.

Answer 15

Now, as before, the arc length is s = r * theta.

first, convert that 100 degree central angle to radians.

Note what JDoe did: He used a conversion factor.

Answer 16

I'll be happy to pick up again where we left off. Hope you won't let this long discussion go to waste. See you again soon?