The Law of Sines
It's a formula that relates side lengths to their opposite angle measure.
We are given a triangle ABC where one of its sides is AC=52.6 cm. Angles A and C are also known, A=44°, C=100°.
We can calculate the third angle by subtracting A+C from 180°:
B = 180° - 44° - 100° = 36°
Now we calculate the side length x by using the law of sines as follows:
[tex]\frac{52.6}{\sin 36}=\frac{x}{\sin 44\~}[/tex]
Solving for x:
[tex]x=52.6\cdot\frac{\sin 44}{\sin 36}[/tex]
Calculating:
[tex]x\text{ = 52.6}\cdot\frac{0.6947}{0.5878}=62.17\operatorname{cm}[/tex]
Thus x = 62.17 cm
