# 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.

Result

b =  12.49 cm
A =  38.682 °
B =  51.318 °
C =  90 °
o =  38.49 cm
S =  62.45 cm2

#### Solution:

$a = 10 \ cm \ \\ c = 16 \ cm \ \\ b = \sqrt{ c^2-a^2 } = \sqrt{ 16^2-10^2 } = 2 \ \sqrt{ 39 } \doteq 12.49 = 12.49 \ \text{ cm }$
$A = 180/ \pi \cdot \ ( \arcsin(a/c)) = 180/ 3.1416 \cdot \ ( \arcsin(10/16)) \doteq 38.6822 = 38.682 ^\circ = 38^\circ 40'56"$
$B = 90 - A = 90 - 38.6822 = 51.318 = 51.318 ^\circ = 51^\circ 19'5"$
$C = 90 = 90 ^\circ$
$o = a+b+c = 10+12.49+16 = \dfrac{ 3849 }{ 100 } = 38.49 = 38.49 \ \text{ cm }$
$S = a \cdot \ b/2 = 10 \cdot \ 12.49/2 = \dfrac{ 1249 }{ 20 } = 62.45 = 62.45 \ cm^2$

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