# Right triangle

Calculate the length of the remaining two sides and the angles in the rectangular triangle ABC if a = 10 cm, angle alpha = 18°40'.

Result

A =  18.667 °
B =  71.333 °
C =  90 °
a =  10 cm
b =  29.6 cm
c =  31.244 cm

#### Solution:

$A=18+40/60=\dfrac{ 56 }{ 3 } \doteq 18.6667 \doteq 18.667 ^\circ \doteq 18^\circ 40'$
$B=90-A=90-18.6667=71.333=71.333 ^\circ =71^\circ 19'59"$
$C=90=90 ^\circ$
$a=10 \ \text{cm}$
$\tan A=a/b \ \\ b=a/\tan( A ^\circ \rightarrow\ \text{rad} )=a/\tan( A ^\circ \cdot \ \dfrac{ \pi }{ 180 } \ )=10/\tan( 18.6666666667 ^\circ \cdot \ \dfrac{ 3.1415926 }{ 180 } \ )=29.59985=29.6 \ \text{cm}$
$c=\sqrt{ a^2+b^2 }=\sqrt{ 10^2+29.5999^2 } \doteq 31.2436 \doteq 31.244 \ \text{cm}$

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