# The right triangle

In the right triangle ABC with 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 result:

c =  11.402 cm
A =  37.874 °
B =  52.126 °

#### Solution:

$b=9 \ \text{cm} \ \\ a=7 \ \text{cm} \ \\ c^2=a^2+b^2 \ \\ \ \\ c=\sqrt{ a^2+b^2 }=\sqrt{ 7^2+9^2 }=\sqrt{ 130 }=11.402 \ \text{cm}$
$\sin A=a/c \ \\ \ \\ A=\dfrac{ 180^\circ }{ \pi } \cdot \arcsin(a/c)=\dfrac{ 180^\circ }{ \pi } \cdot \arcsin(7/11.4018)=37.874 ^\circ =37^\circ 52'26"$
$B=90-A=90-37.874=52.126 ^\circ =52^\circ 7'34"$

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