Answer to Question #272080 in Trigonometry for nath smith

Question

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

2. A= 82°, b=100°, c=78° Find: B

Answer 1

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

$$cos (a) = cos(b) * cos (c)+sin(b)*sin(c)*cos(A)$$

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

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

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

$$a=arccos(0.02)=88.85°$$

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

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

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

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

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

$$B=arcsin(0.9754)=77.27°$$

Answer: 77.27°