I have a triangle with C = 90 degrees and a c = 166 cm and last but not least an a = 130,96 cm
which formulas and calculations do i have to do to find out the missing lengths (A,b, B)
I have a triangle with C = 90 degrees and a c = 166 cm and last but not least an a = 130,96 cm
which formulas and calculations do i have to do to find out the missing lengths (A,b, B) ?
$$\\\small{\text{$
\begin{array}{rcl}
\sin{(A)}&=&\dfrac{a}{c}\\\\
\sin{(A)}&=&\dfrac{ 130.96~\rm{cm} }{ 166.00~\rm{cm} }\\\\
\sin{(A)}&=&0.78891566265\\\\
A&=&52.0842936445\ensurement{^{\circ}}
\end{array}
$}}\\\\\\
\small{\text{$
\begin{array}{rcl}
B&=& 90\ensurement{^{\circ}} - A\\\\
B&=& 90\ensurement{^{\circ}} - 52.0842936445\ensurement{^{\circ}}\\\\
B&=& 37.9157063555\ensurement{^{\circ}}\\\\
\end{array}
$}}\\\\
\\\small{\text{$
\begin{array}{rcl}
\sin{(B)}&=&\dfrac{b}{c}\\\\
b &=& c\cdot \sin{(B)}\\\\
b &=& 166.00~\rm{cm} \cdot \sin{(37.9157063555\ensurement{^{\circ}})}\\\\
b &=& 166.00~\rm{cm} \cdot 0.61450148676 \\\\
b &=& 102.01~\rm{cm} \\\\
\end{array}
$}}$$
I have a triangle with C = 90 degrees and a c = 166 cm and last but not least an a = 130,96 cm
which formulas and calculations do i have to do to find out the missing lengths (A,b, B) ?
$$\\\small{\text{$
\begin{array}{rcl}
\sin{(A)}&=&\dfrac{a}{c}\\\\
\sin{(A)}&=&\dfrac{ 130.96~\rm{cm} }{ 166.00~\rm{cm} }\\\\
\sin{(A)}&=&0.78891566265\\\\
A&=&52.0842936445\ensurement{^{\circ}}
\end{array}
$}}\\\\\\
\small{\text{$
\begin{array}{rcl}
B&=& 90\ensurement{^{\circ}} - A\\\\
B&=& 90\ensurement{^{\circ}} - 52.0842936445\ensurement{^{\circ}}\\\\
B&=& 37.9157063555\ensurement{^{\circ}}\\\\
\end{array}
$}}\\\\
\\\small{\text{$
\begin{array}{rcl}
\sin{(B)}&=&\dfrac{b}{c}\\\\
b &=& c\cdot \sin{(B)}\\\\
b &=& 166.00~\rm{cm} \cdot \sin{(37.9157063555\ensurement{^{\circ}})}\\\\
b &=& 166.00~\rm{cm} \cdot 0.61450148676 \\\\
b &=& 102.01~\rm{cm} \\\\
\end{array}
$}}$$