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AC = 12√3. Find BC and AB. Write answer in simplest form.

AC = 12√3. Find BC and AB. Write answer in simplest form.-example-1
User Krflol
by
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1 Answer

14 votes
14 votes

BC = a

AC = b= 12√3

AB =c

A= 30°

B=60°

C=90°

Using the sine rule


\frac{\sin\text{ A}}{a}=(\sin B)/(b)

substitute the values into the above


(\sin30)/(a)=\frac{\sin 60}{12\sqrt[]{3}}
((1)/(2))/(a)=\frac{\frac{\sqrt[]{3}}{2}}{12\sqrt[]{3}}
(1)/(2* a)=\frac{\sqrt[]{3}}{2*12\sqrt[]{3}}
(1)/(2a)=\frac{\sqrt[]{3}}{24\sqrt[]{3}}
(1)/(2a)=(1)/(24)

cross multiply


2a=\text{ 24}
a=12

Therefore BC = 12

Let's proceed to find AB


(\sin A)/(a)=(\sin C)/(c)
(\sin30)/(12)=(\sin 90)/(c)
((1)/(2))/(12)=(1)/(c)
(1)/(2*12)=(1)/(c)
(1)/(24)=(1)/(c)

cross-multiply


c=24

User Bheinz
by
2.8k points