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Mathematics 16 Online
OpenStudy (anonymous):

I still need help on one more please

OpenStudy (anonymous):

I got 8.49 for the missing side but since one side is sqrt. im confused @jim_thompson5910

jimthompson5910 (jim_thompson5910):

the missing side should be a whole number

jimthompson5910 (jim_thompson5910):

hint: we have a 30-60-90 triangle

OpenStudy (anonymous):

so then just 8?

jimthompson5910 (jim_thompson5910):

not quite

OpenStudy (anonymous):

4?

jimthompson5910 (jim_thompson5910):

let me know if this helps or not http://hotmath.com/hotmath_help/topics/30-60-90-triangles/triangle1.gif

OpenStudy (anonymous):

a^2 + b^2=c^2 because it is a right angle. So just do (6)^2+6rad(3)= and square root the answer.

OpenStudy (anonymous):

i got 6

OpenStudy (anonymous):

and that really did help clear things up

OpenStudy (anonymous):

didnt**

jimthompson5910 (jim_thompson5910):

you should get 12

jimthompson5910 (jim_thompson5910):

or you can use the pythagorean theorem a^2 + b^2 = c^2 6^2 + (6*sqrt(3))^2 = c^2 36 + 36*3 = c^2 36 + 108 = c^2 144 = c^2 c^2 = 144 c = sqrt(144) c = 12

jimthompson5910 (jim_thompson5910):

so again, the missing side is 12

OpenStudy (anonymous):

okay

jimthompson5910 (jim_thompson5910):

so, cos(B) = adj/hyp cos(B) = 6/12 cos(B) = 1/2

OpenStudy (anonymous):

2.44 as my answer

jimthompson5910 (jim_thompson5910):

idk how you got that

OpenStudy (anonymous):

me neither

jimthompson5910 (jim_thompson5910):

do you see how I got 1/2 ?

OpenStudy (anonymous):

yeah

OpenStudy (anonymous):

one side is \(6\) the other sides is \(6\sqrt3\) that makes the hypotenuse \(2\times 6=12\) since the ratios of such a right triangle (30-60-90\) are \[1:\sqrt3:2\] meaning the hypotenuse is twice the short leg

OpenStudy (anonymous):

Sqrt.3/2 would be the right answer then?

OpenStudy (anonymous):

what are you trying to find, sine or cosine

OpenStudy (anonymous):

cos

OpenStudy (anonymous):

the sine is \(\frac{\sqrt3}{2}\) as in "opposite over hypotenuse"

OpenStudy (anonymous):

the cosine is \(\frac{1}{2}\) oh hold on, let me check which angle it is

OpenStudy (anonymous):

yeah angle B, cosine is \(\frac{1}{2}\)

OpenStudy (anonymous):

okay thank you(:

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