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Answer in Trigonometry

Author:
October 16th, 2022

 Solve the following spherical triangle using Law of Sine and Cosine.

2. A= 82°, b=100°, c=78° Find: B

 

Using the Law of Cosine, we can find the side a.

 

“cos (a) = cos(b) * cos (c)+sin(b)*sin(c)*cos(A)”

“cos(a)= cos(100u00b0) * cos (78u00b0)+sin(100u00b0)*sin(78u00b0)*cos(82u00b0)”

“cos(a)= -0.74 * 0.208+0.985*0.978*0.139=”

“=-0,154+0.134=0.02”

“a=arccos(0.02)=88.85u00b0”

And then, using the Law of Sines, we can find B.

 

“sin(a)/sin(A)=sin(b)/sin(B)”

“sin(B)=sin(b)*sin(A)/sin(a)”

“sin(B)=sin(100u00b0)*sin(82u00b0)/sin(88.85u00b0)”

“sin(B)=0.9848*0.9903/0.9998=0.9754”

“B=arcsin(0.9754)=77.27u00b0”

Answer: 77.27°

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