By law of sines and law of cosine and knowing that a = 530 inches, b = 680 inches and ∠C = 102°, the angle B has a measure of approximately 44.733°.
In this question we can determine the missing angle by means of the law of sines and the law of cosine. First we use the law of cosine:
[tex]c = \sqrt{a^{2}+b^{2}-2\cdot a\cdot b \cdot \cos C}[/tex] (1)
[tex]c = \sqrt{530^{2}+680^{2}-2\cdot (530)\cdot (680)\cdot \cos 102^{\circ}}[/tex]
c ≈ 945.073 in
Lastly, we determine the value of the angle B by the law of sines:
[tex]\frac{C}{\sin C} = \frac{B}{\sin B}[/tex] (2)
[tex]\frac{945.073}{\sin 102^{\circ}} = \frac{680}{\sin B}[/tex]
B ≈ 44.733°
By law of sines and law of cosine and knowing that a = 530 inches, b = 680 inches and ∠C = 102°, the angle B has a measure of approximately 44.733°.
The statement is poorly formatted. Correctly formatted is shown below:
In ΔABC, a = 530 inches, b = 680 inches and ∠C = 102°. Find ∠B to the nearest degree.
To learn more on triangles: https://brainly.com/question/2773823
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