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# Practice question help

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

Apr 4, 2020

#1
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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

Apr 4, 2020
#2
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Thanks! Still confused though. Isn't there only one answer as you found the angles already?

Apr 5, 2020
#3
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I think there is only one.