\(Sin 0.25 = {r \over r+384403}\)

That equals 1684.62, but how?

I've been stuck on it for an hour and just cannot figure it out

Guest Jun 20, 2017

#1**+2 **

Sin 0.25 = {r \over r+384403}

\(Sin( 0.25) = {r \over r+384403}\\ ( r+384403)Sin( 0.25) =r\\ rSin( 0.25) +384403Sin( 0.25) =r\\ 384403Sin( 0.25) =r-rSin( 0.25) \\ 384403Sin( 0.25) =r(1-Sin( 0.25)) \\ \frac{384403Sin( 0.25)}{(1-Sin( 0.25)) } =r\\ r=\frac{384403Sin( 0.25)}{(1-Sin( 0.25)) } \\ \)

(384403*sin(0.25))/(1-sin(0.25) = approx 126366.362

Which is different from your answer :)

Melody Jun 20, 2017

#2**0 **

**Note: Melody used "radians" for sin(.25). I used "degrees" to get the same answer that you have:**

Solve for r:

0.00436331 = r/(r + 384403)

0.00436331 = r/(r + 384403) is equivalent to r/(r + 384403) = 0.00436331:

r/(r + 384403) = 0.00436331

Multiply both sides by r + 384403:

r = 0.00436331 (r + 384403)

Expand out terms of the right hand side:

r = 0.00436331 r + 1677.27

Subtract 0.00436331 r from both sides:

0.995637 r = 1677.27

Divide both sides by 0.995637:

**Answer: | r = 1684.62**

Guest Jun 20, 2017