Answer:
a = 22, b = 11
Step-by-step explanation:
The given triangle is a 30-60-90 right triangle
We can use the law of sines to determine the missing sides
Law of Sines
The ratio of the side of a triangle to the sine of the angle opposite is the same for all sides and their opposite angles
Applying this law to the given figure provides:
[tex]\dfrac{a}{\sin 90} = \dfrac{b}{\sin30} = \dfrac{11\sqrt{3}}{\sin 60}[/tex]
We have the following sine values:
[tex]\sin 90 = 1\\\\\sin 30 = \dfrac{1}{2}\\\\\sin 60 = \dfrac{\sqrt{3}}{2}[/tex]
Plugging in these values we get
[tex]\dfrac{a}{1} = \dfrac{b}{1/2} = \dfrac{11\sqrt{3}}{\sqrt{3}/2}[/tex]
Simplifying this becomes
a = 2b = 22
Therefore
a = 22
2b = 22 => b = 11
