In triangle ABC, B = 30^\circ, AB = 150, and AC = 50 sqrt3. Find the sum of all possible values of BC.
+658 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.
