Question

A park maintenance person stands 16 m from a circular monument. If you assume her lines of sight form tangents to the monument and make an angle of 34°, what is the measure of the arc of the monument that her lines of sight intersect?

A) 68
B) 292
C) 146
D) 17

Thanks!

Answer 1

Any luck?

Answer 2

Yeah...I think I've got it. Give me a minute to figure out my notes.

Answer 3

great!

Answer 4

I have to get ready for work. But if you come up with something, i'll come back to the computer and reward you! So please don't worry!

Answer 5

k...

Answer 6

Here's the diagram my reasoning is based on...

Answer 7

We know that the angle between the tangents is 34 degrees, so m(angle CET)=17. Since m(angle CTE) is 90 degrees (being tangent), the internal sector formed by angle ECT is 73 degrees. So the arc in question has angle measure 146 degrees.

That's one of your choices...not sure if it's correct. You might be looking for the actual arc length...

If you only need the arc angle measure, stop here...otherwise, I'll continue.

Answer 8

The formula for the measure of an arc of a circle is\[s=\pi r \theta/180\]where theta is the arc angle in degrees.

So, we need to know the radiusof the circular monument which, unfortunately, was not given to us.

I calculate it, we'll use similar triangles.

Answer 9

Since we know that triangle ECT is right, dropping a perpendicular from point I (not labeled...it's where EC intersects the circle) to ET, creates similar triangle EIT'

We can find the length of IT' using trigonometry.
\[IT'=16\sin(17)\approx4.68\]so the ratio 16/4.68 = (16+r)/r

Solving this for r, we get\[16r\approx4.86(16)+4.68r\]\[11.32r\approx74.88\]\[r\approx6.61\]
Using this in the above formula gets us\[s=\pi r\theta/180\approx\pi(6.61)(146)/180\approx16.9\]
The given answer of 17 is really close. :)

Answer 10

Based on what was given to you ...namely the distance from the monument, I'm sure this is what you need. If not, use the first one.
:)

Cheers!

Answer 11

Thanks man!

Answer 12

no problem. hope it helps.

Answer 13

Oh boy, does it!

Answer 14

You understood the steps taken?

Answer 15

Not really, cause I'm rushing, but I'm gonna to come back later and look it over. I'm pretty sure I'll be able to understand all it then. :)

Answer 16

If not, leave another comment and when I get back on, I'll try to clear it up.

Answer 17

Thank you!