Question

How do i solve for c as a radical?
What I have done so far and the question are both below.

Answer 1

@jim_thompson5910

Answer 2

\[\sin(45^\circ)=\frac{\sqrt2}{2}=\frac{c}{8}\] solve \[\frac{\sqrt2}{2}=\frac{c}{8}\] for \(c\)

Answer 3

wait where did the sqrt of 2 over 2 come from?

Answer 4

@satellite73

Answer 5

oh wait never mind i got it
its 8 sqrt 2

Answer 6

Use the unit circle
https://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Unit_circle_angles_color.svg/2000px-Unit_circle_angles_color.svg.png
Locate the angle 45 degrees.
The point that corresponds to this angle has a y coordinate of \(\LARGE \frac{\sqrt{2}}{2}\)


So that's why
\[\Large \sin(45^{\circ}) = \frac{\sqrt{2}}{2}\]

Answer 7

thanks

Answer 8

the answer to the equation @satellite73 posted is not 8*sqrt(2)

Answer 9

wait but hypotenuse is sqrt2 times a or b

Answer 10

\[\Large \sin(45^{\circ}) = \frac{8}{c}\]
\[\Large \frac{\sqrt{2}}{2} = \frac{8}{c}\]
\[\Large c*\sqrt{2} = 2*8\]
\[\Large c*\sqrt{2} = 16\]
\[\Large c = \frac{16}{\sqrt{2}}\]
\[\Large c = \frac{16\sqrt{2}}{\sqrt{2}*\sqrt{2}}\]
\[\Large c = \frac{16\sqrt{2}}{2}\]
\[\Large c = 8\sqrt{2}\]
I see what you mean now