Right triangle eq2

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

Correct answer:

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

Step-by-step explanation:

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$$\begin{gathered} b=2\cdot S\mathrm{/}a=2\cdot 210\mathrm{/}21=20 \\ b=a_2=20 \end{gathered}$$

$c=\sqrt{a^2+b^2}=\sqrt{21^2+20^2}=29$

$A={\displaystyle \frac{180\mathrm{°}}{\pi }}\cdot \arcsin (a\mathrm{/}c)={\displaystyle \frac{180\mathrm{°}}{\pi }}\cdot \arcsin (21\mathrm{/}29)=46.3972\text{°}=46\mathrm{°}23^{\mathrm{\prime }}50\mathrm{"}$

$B={\displaystyle \frac{180\mathrm{°}}{\pi }}\cdot \arcsin (b\mathrm{/}c)={\displaystyle \frac{180\mathrm{°}}{\pi }}\cdot \arcsin (20\mathrm{/}29)=43.6028\text{°}=43\mathrm{°}36^{\mathrm{\prime }}10\mathrm{"}$

$C=90=90\text{°}$

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