In triangle ABC, B = 30^\circ, AB = 150, and AC = 50 sqrt3. Find the sum of all possible values of BC.

Guest Apr 4, 2020

#1**+1 **

**Angle B**

It is given as 30 degrees

**Angle C**

By law of sines:

\(\frac{sin(30^\circ)}{50\sqrt{3}}=\frac{sin(C^\circ)}{150}\)

asin(150*(sin(30)/(50*sqrt(3))) = 60

Solving, we get angle C = 60 degrees.

**Angle A**

Since all angles in a triangle add to 180, angle A is 180 - 30 - 60 = 90.

**BC**

To solve for BC, try all of these methods (you may have different results depending on the method)

- Pythagorean theorem

- 30 - 60 - 90 triangle

- Law of sines

- Law of cosines

The answer is all the different values of BC added up.

AnExtremelyLongName Apr 4, 2020