Answer to Question #272080 in Trigonometry for nath smith

Question #272080

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

2. A= 82°, b=100°, c=78° Find: B


1
Expert's answer
2022-02-09T13:33:00-0500

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(b) * cos (c)+sin(b)*sin(c)*cos(A)

cos(a)=cos(100°)cos(78°)+sin(100°)sin(78°)cos(82°)cos(a)= cos(100°) * cos (78°)+sin(100°)*sin(78°)*cos(82°)

cos(a)=0.740.208+0.9850.9780.139=cos(a)= -0.74 * 0.208+0.985*0.978*0.139=

=0,154+0.134=0.02=-0,154+0.134=0.02

a=arccos(0.02)=88.85°a=arccos(0.02)=88.85°

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


sin(a)/sin(A)=sin(b)/sin(B)sin(a)/sin(A)=sin(b)/sin(B)

sin(B)=sin(b)sin(A)/sin(a)sin(B)=sin(b)*sin(A)/sin(a)

sin(B)=sin(100°)sin(82°)/sin(88.85°)sin(B)=sin(100°)*sin(82°)/sin(88.85°)

sin(B)=0.98480.9903/0.9998=0.9754sin(B)=0.9848*0.9903/0.9998=0.9754

B=arcsin(0.9754)=77.27°B=arcsin(0.9754)=77.27°

Answer: 77.27°


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