Answer:
[tex]b=7\sqrt{3}[/tex]
Step-by-step explanation:
First, we need to use the law of sines in order to find the measure of side a. Recall that the law of sines states: [tex]\frac{a}{sinA} =\frac{c}{sinC}[/tex]
Using this, we can input our three known values into this equation
[tex]\frac{a}{sin(90)} =\frac{7}{sin(30)} \\\\a=\frac{7sin(90)}{sin(30)}[/tex]
When put into a calculator, [tex]a=14[/tex]
Now that we have two sides of a right triangle, we can use the Pythagorean Theorem to solve for side b.
Recall that the Pythagorean Theorem states: [tex]a^2+b^2=c^2[/tex]
In this case, we need to solve for B
[tex]b^2=c^2-a^2\\\\b=\sqrt{c^2-a^2}[/tex]
In the case of this equation, c=14 and a=7 (I know kind of confusing to have them reversed)
[tex]b=\sqrt{14^2-7^2} \\\\b=\sqrt{196-49} \\\\b=\sqrt{147} \\\\b=7\sqrt{3}[/tex]
