The aspect ratio

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

Correct answer:

A =  90 °
B =  67.3801 °
C =  22.6199 °

Step-by-step explanation:

$$\begin{gathered} a:b:c=13:12:5 \\ a=13x \\ b=12x \\ c=5x \\ {a}^2=b^2+c^2 \\ (13x{)}^2=(12x{)}^2+(5x{)}^2 \\ 13^2=12^2+5^2 \\ 169=144+25 \\ 169 \\ A=90=90\text{°} \end{gathered}$$

$$\begin{gathered} \sin B={\displaystyle \frac{b}{a}}={\displaystyle \frac{12x}{13x}} \\ B={\displaystyle \frac{180\mathrm{°}}{\pi }}\cdot \arcsin (12\mathrm{/}13)=67.3801\text{°}=67\mathrm{°}22^{\mathrm{\prime }}49\mathrm{"} \end{gathered}$$

$C=90-B=90-67.3801=22.6199\text{°}=22\mathrm{°}37^{\mathrm{\prime }}11\mathrm{"}$

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