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Find the length $BC$, to two decimal places.

 

 Feb 16, 2024

Best Answer 

 #2
avatar+128732 
+1

Just a slight error by EnormousBighead....

 

BC has to be >  5 because angle A > angle B

 

AC/ sin 34  = BC / sin 108

 

5 / sin 34 = BC / sin 108

 

BC  = 5*sin 108 / sin 34  ≈ 8.50

 

 

 

 

cool cool cool  

 Feb 16, 2024
 #1
avatar
+1

\(\angle ABC=180-(\angle BAC+\angle BCA)=34^\circ\)

using \(\sin\) rule of triangles:

\(\Large\frac{AC}{\sin{\angle{ABC}}}=\frac{BC}{\sin{\angle{BAC}}}\\ \Large\Rightarrow BC=\frac{5\sin{34^\circ}}{\sin{108^\circ}}\approx3\)

Exact value is \(2.93985\)

 Feb 16, 2024
 #2
avatar+128732 
+1
Best Answer

Just a slight error by EnormousBighead....

 

BC has to be >  5 because angle A > angle B

 

AC/ sin 34  = BC / sin 108

 

5 / sin 34 = BC / sin 108

 

BC  = 5*sin 108 / sin 34  ≈ 8.50

 

 

 

 

cool cool cool  

CPhill Feb 16, 2024

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