# Right triangle eq2

Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70.

a =  21
b =  20
c =  29
A =  46.3972 °
B =  43.6028 °
C =  90 °

### Step-by-step explanation:

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$c=\sqrt{{a}^{2}+{b}^{2}}=\sqrt{2{1}^{2}+2{0}^{2}}=29$
$A=\frac{180\mathrm{°}}{\pi }\cdot \mathrm{arcsin}\left(a\mathrm{/}c\right)=\frac{180\mathrm{°}}{\pi }\cdot \mathrm{arcsin}\left(21\mathrm{/}29\right)=46.3972\text{°}=46\mathrm{°}2{3}^{\mathrm{\prime }}50\mathrm{"}$
$B=\frac{180\mathrm{°}}{\pi }\cdot \mathrm{arcsin}\left(b\mathrm{/}c\right)=\frac{180\mathrm{°}}{\pi }\cdot \mathrm{arcsin}\left(20\mathrm{/}29\right)=43.6028\text{°}=43\mathrm{°}3{6}^{\mathrm{\prime }}10\mathrm{"}$
$C=90=90\text{°}$

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