An unmanned rescue submarine is scanning the ocean floor from a height of 150 feet above the floor. The field of view of the scan is 40 degrees. What is the diameter of the circle captured by the scan at any one moment?
How would I do this? Please help!

- anonymous

- chestercat

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- freeG13

80 degrees is the diameter

- anonymous

Wouldn't the diameter be in feet?

- freeG13

yes sorry I forgot to put ft in the middle for 80 ft degrees

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## More answers

- amistre64

|dw:1433272647169:dw|

- anonymous

@amistre64 what equation would I use to find r?

- amistre64

something triggy i believe, what trig function do you know?

- amistre64

perferably the one that uses the legs of the right triangle as its ratio

- anonymous

I am not sure which one that would be, cos sin or tan, this problem is a lot harder than any they've given us before.

- amistre64

well, we need one of those, define all all three for me, to the best of your recollection, ill correct if needed

- anonymous

sin - o/s*h
cos - a/c*h
tan - o/t*a

- anonymous

it would be tan?

- amistre64

tangent yes
so: tan(a) = r/h what is r? and for that matter, what would a be as well?

- amistre64

your formulas are odd to me,
soh
cah
toa
is a memory device, and it seems that youve got them kind of in order ...
toa would referet o: tan = o/a

- amistre64

|dw:1433273093727:dw|

- anonymous

why is 40/2? instead of 40?

- amistre64

40 is our angle from outside to outside of the circle|dw:1433273181681:dw|

- anonymous

ohhh!

- amistre64

ideally, our sub is above the center of it ....

- anonymous

How would I find r? tan of angle?

- amistre64

tan(a) = r/h
multiply both sides by h
h tan(a) = r, and the diameter is just 2r

- amistre64

we know h and a, the rest is a calculator

- anonymous

would the diameter then be 671.15? That seems a little high

- anonymous

tan(20) * 150 = r * 2 =671

- amistre64

150*tan(20) = radius
2*150*tan(20) = diameter
you have your calculator in radian mode

- amistre64

put it in degree mode, or else convert, multiply by 180/pi

- anonymous

multiply 671 by 180/pi?

- amistre64

sure, thats a simple fix, itll define it in degree mode that way

- anonymous

109.2

- amistre64

lets take out human error ...
http://www.wolframalpha.com/input/?i=2*150*tan%2820deg%29

- amistre64

yes, thats better

- anonymous

perfect thank you!

- amistre64

yw

- anonymous

Would you be willing to help with a similar one?

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