The aspect ratio

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

Correct result:

A =  90 °
B =  67.38 °
C =  22.62 °

Solution:

a:b:c=13:12:5 a=13x b=12x c=5x  a2=b2+c2 (13x)2=(12x)2+(5x)2 132=122+52 169=144+25 169  A=90=90
sinB=ba=12x13x  B=180πarcsin(12/13)=67.38=672249"\sin B=\dfrac{ b }{ a }=\dfrac{ 12x }{ 13x } \ \\ \ \\ B=\dfrac{ 180^\circ }{ \pi } \cdot \arcsin(12/13)=67.38 ^\circ =67^\circ 22'49"
C=90B=9067.3801=113150=22.62=223712"C=90-B=90-67.3801=\dfrac{ 1131 }{ 50 }=22.62 ^\circ =22^\circ 37'12"

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Check out our ratio calculator.
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

 
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