Right triangle

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

Final 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:

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

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

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

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

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

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

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