Question

Ill give brainlest And extra points​

Answer 1

Answer:

$b=7\sqrt{3}$

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: $\frac{a}{sinA} =\frac{c}{sinC}$

Using this, we can input our three known values into this equation

$\frac{a}{sin(90)} =\frac{7}{sin(30)} \\\\a=\frac{7sin(90)}{sin(30)}$

When put into a calculator, $a=14$

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: $a^2+b^2=c^2$

In this case, we need to solve for B

$b^2=c^2-a^2\\\\b=\sqrt{c^2-a^2}$

In the case of this equation, c=14 and a=7 (I know kind of confusing to have them reversed)

$b=\sqrt{14^2-7^2} \\\\b=\sqrt{196-49} \\\\b=\sqrt{147} \\\\b=7\sqrt{3}$