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# im confused on this ;-;

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hi!! this is the problem i cant seem to get through today:

In triangle $ABC,$ $\angle BCA = \frac{\pi}{6}, AB = 4$ and $AC = 10$.

Find the sum of all distinct possible values of $BC.$ If there are no possible values, enter $0$.

ive done th eprevious like four parts of the problem but this part is really confusing to me and i just keep getting it wrong. thank you sooo so much in advance for the help!!! :) <3

Sep 6, 2023

#1
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Hello heartSTORM907!

There is no result for the distance BC.

$$\overline{BC}\in \{\}\\ \sum(\ \overline{BC}\ )=0\ as\ specified\ in\ the\ task.$$ !.

Sep 6, 2023
#2
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OH MY GOD i almost completely forgot about that part.... i kept thinking i was doing something wrong lol

thank you so so so much!!!!

Sep 6, 2023
#3
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angle BCA =  30°

Using the Law of Sines

sin BCA / AB  = sin ABC / 10

sin (30°) / 4 =  sin ABC /10

(1/2) / 4  = sin ABC /10

(1/8)  = sin ABC  /10

(10/8) = sin ABC

(5/4)  = sin ABC        { impossible}   Sep 6, 2023
#4
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thank you!!! that was really helpful!

heartSTORM907  Sep 6, 2023