# The aspect ratio

The aspect ratio of the rectangular triangle is 13: 12: 5. Calculate the internal angles of the triangle.

Result

A =  90 °
B =  67.38 °
C =  22.62 °

#### Solution:

$a:b:c = 13:12:5 \ \\ a = 13x \ \\ b = 12x \ \\ c = 5x \ \\ \ \\ a^2 = b^2+c^2 \ \\ (13x)^2 = (12x)^2 + (5x)^2 \ \\ 13^2 = 12^2 + 5^2 \ \\ 169 = 144 + 25 \ \\ 169 \ \\ \ \\ A = 90 = 90 ^\circ$
$\sin B = \dfrac{ b }{ a } = \dfrac{ 12x }{ 13x } \ \\ \ \\ B = \dfrac{ 180^\circ }{ \pi } \cdot \arcsin(12/13) \doteq 67.3801 = 67.38 ^\circ = 67^\circ 22'49"$
$C = 90-B = 90-67.3801 = \dfrac{ 1131 }{ 50 } = 22.62 = 22.62 ^\circ = 22^\circ 37'12"$

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