$\backslash$table$[[$r$1$a$,$r$1$b$,$r$2,$r$2$P$,$r$3,],[$given$,$given,given,$100,$r$3,$cm$],[$theta$\_1$a$,$theta$\_1$b$,$theta$\_2,$theta$\_2$P$,$theta$\_3,],[$given$,$given,given,theta$\_2,$theta$\_3,$degrees$]]$

An adjustable exercise bench shown in the picture, schematic and vector model. You need to select pin locations to adjust the bench to fixed angles $($such as $0,30,60,90$ degrees$).$ Solve for the length of the adjustable length bar $($vector r$3)$ for a given bench angle. ALL ANGLES GIVEN IN DEGREES. ENTER ANSWER IN DEGREES.

Solve for adjustable bar angle $($theta$3)$ resulting from the loop closure solution. Use the method covered in class.

Assume that the angle of the bench $($theta$2)$ is given. Write your loop equation in a clock$-$wise direction.

Given data is here and on figure and table. $r1a=54$;$r1b=76$;$r2=160$; theta $2=15$;

Answer:

$,(29\mathrm{.}38)$

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since vectors $1$a$,1$b$,2$ show up negative in the loop equation $($assuming your loop is CW$),$ you need to be sure and place negatives with the magnitudes of these vectors in your equations.

r$3\_$vec $=$ r$1$a$\_$vec $+$ r$1$b$\_$vec $+$ r$2\_$vec; r$1$a$,$ r$1$b$,$ r$2$ all known. Solve for r$3/$ theta$3$ in the same way you would for rk

Show me how to get the answer shown please!