## Question:

The sphere of weight $W$ rests between the smooth inclined planes. Determine the reaactions at the supports.

Given:

$W$ = $10$ $Ib$

${ \theta }_{ 1 }$ = $105$ $deg$

${\theta }_{ 2 }$ = $45$ $deg$

## Step-by-step

Initial guesses

${ N }_{ A }$ = $1$ $Ib\quad { N }_{ A }$ = $1$ $Ib$

Given:

${ N }_{ B }\cos { \left( { \theta }_{ 1 }-90deg \right) } -{ N }_{ A }\cos { \left( { \theta }_{ 2 } \right) }$ = $0$

${ N }_{ A }\sin { \left( { \theta }_{ 2 } \right) } -{ N }_{ B }\sin { \left( { \theta }_{ 1 }-90deg \right) } -W$= $0$

$\left( \begin{matrix} { N }_{ A } \\ { N }_{ B } \end{matrix} \right)$ = $Find$(${ N }_{ A },{ N }_{ B }$)$\quad \quad \quad \left( \begin{matrix} { N }_{ A } \\ { N }_{ B } \end{matrix} \right)$ =$\left( \begin{matrix} 19.3 \\ 14.1 \end{matrix} \right)$ $Ib$