Because the 50 is your Adjacent Side not Hypot as I said (look at the angles to see which side is the hypot)
Im going to go look at my thread now maybe somones helped me on it take a look if you know statistics and probability.
http://www.mathhelpforum.com/math-he...tribution.html
Hello, 4AM!
$\displaystyle PQ = 50,\;\;\angle PSR = 32^o,\;\;\angle QSR = 216^o.\;\;\text{Find }RS.$Code:- P * : | * : | * : x | * : | * 50 | 32° * : R * - - - - - - - - - - - * S : | 26° * : 50-x | * : | * - Q *
Let $\displaystyle x \:=\:PR \quad\Rightarrow\quad 50-x\:=\:RQ$
In right triangle $\displaystyle PRS\!:\;\;\tan32^o \:=\:\frac{x}{RS} \quad\Rightarrow\quad x \:=\:RS\!\cdot\!\tan32^o\;\;{\color{blue}[1]}$
In right triangle $\displaystyle QRS\!:\;\;\tan26^o \:=\:\frac{50-x}{RS} \quad\Rightarrow\quad x \:=\:50-RS\!\cdot\!\tan26^o\;\;{\color{blue}[2]}$
Equate [1] and [2]: .$\displaystyle RS\!\cdot\tan32^o \:=\:50 - RS\!\cdot\!\tan26^o \quad\Rightarrow\quad RS\!\cdot\!\tan32^o + RS\!\cdot\!\tan26^o \:=\:50$
Factor: .$\displaystyle RS\!\cdot\!(\tan32^o+\tan26^o) \:=\:50 \quad\Rightarrow\quad RS \:=\:\frac{50}{\tan32^o+\tan26^o}$
Therefore: .$\displaystyle RS \;\approx\;44.94$
$\displaystyle \angle STW = 38.8^o,\;\;\angle STV = 53.8^o,\;\;VW = 12.5$ . Find $\displaystyle TU.$Code:T * - - - - - - - S | * * 38.8° | *15°* | * * | * * | * * | * * | 53.8° * 38.8° * * - - - - - - - * - - - - - - - * U V 12.5 W
We have: .$\displaystyle \angle STW = 38.8^o \quad\Rightarrow\quad \angle TWU = 38.8^o$
Since $\displaystyle \angle STV = 58.8^o$, then $\displaystyle \angle WTV = 15^o\:\text{ and }\:\angle TVU = 53.8^o$
In $\displaystyle \Delta TVW$, use the Law of Sines:
. . $\displaystyle \frac{TV}{\sin38.8^o} \:=\:\frac{12.5}{\sin15^o} \quad\Rightarrow\quad TV \:\approx\:30.36$
In right triangle $\displaystyle TUV\!:\;\;\sin53.8^o \:=\:\frac{TU}{TV} \quad\Rightarrow\quad TU \:=\:30.26\!\cdot\!\sin53.8^o$
Therefore: .$\displaystyle TU \;\approx\;24.42$