Right triangle

Calculate the missing side b and interior angles, perimeter, and area of ​​a right triangle if a=10 cm and hypotenuse c = 16 cm.

Correct answer:

b =  12.49 cm
A =  38.6822 °
B =  51.3178 °
C =  90 °
o =  38.49 cm
S =  62.45 cm²

Step-by-step explanation:

$$\begin{gathered} a=10\text{ cm } \\ c=16\text{ cm } \\ b=\sqrt{c^2-a^2}=\sqrt{16^2-10^2}=2\sqrt{39}=12.49\text{ cm} \end{gathered}$$

$A=180\mathrm{/}\pi \cdot (\arcsin (a\mathrm{/}c))=180\mathrm{/}3.1416\cdot (\arcsin (10\mathrm{/}16))=38.6822^{\circ }=38^{\circ }40^{\mathrm{\prime }}56\mathrm{"}$

$B=90-A=90-38.6822=51.3178^{\circ }=51^{\circ }19^{\mathrm{\prime }}4\mathrm{"}$

$C=90=90^{\circ }$

$o=a+b+c=10+12.49+16=38.49\text{ cm}$

$S=a\cdot b\mathrm{/}2=10\cdot 12.49\mathrm{/}2=10\sqrt{39}=62.45{\text{cm}}^2$

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