The right triangle

In the right triangle ABC with a right angle at C, we know the side lengths AC = 9 cm and BC = 7 cm. Calculate the length of the remaining side of the triangle and the size of all angles.

Correct answer:

c =  11.4018 cm
A =  37.875 °
B =  52.125 °

Step-by-step explanation:

$$\begin{gathered} b=9\text{cm} \\ a=7\text{cm} \\ {c}^2=a^2+b^2 \\ c=\sqrt{a^2+b^2}=\sqrt{7^2+9^2}=\sqrt{130}=11.4018\text{cm} \end{gathered}$$

$$\begin{gathered} \sin A=a/c \\ A=\frac{180°}{\pi }\cdot \arcsin (a/c)=\frac{180°}{\pi }\cdot \arcsin (7/11.4018)=37.875^{\circ }=37°52^{\prime }30" \end{gathered}$$

$B=90-A=90-37.875=52.125^{\circ }=52°7^{\prime }30"$

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