Answer:
b = 7.76
Step-by-step explanation:
ABC is a triangle. In a triangle, we have the formula as following:
+) Cosine ∠An angle = [tex]\frac{Adjacent side a^{2} + Adjacent side b^{2} - Opposite side^{2} }{ 2 * Adejacent side a* Adejacent side b}[/tex]
As we can see in the figure, Angle B has:
+) Adjacent side a is BA = 10
+) Adjacent side b is BC = 12
+) Opposite side is AC = b
The measure of Angle B is 40°.
Replace these into the formula, we have:
+) Cosine ∠B = [tex]\frac{AB^{2}+BC^{2}-AC^{2} }{2ABBC}[/tex]
⇔ Cosine 40° = [tex]\frac{10^{2}+12^{2} -b^{2} }{2*10*12}[/tex]
⇔ 0.766 = [tex]\frac{244 - b^{2} }{240}[/tex]
⇔ 0.766 x 240 = 244- b^2
⇔ 183.84 = 244 -b^2
⇔ b^2 = 244 - 183.84 = 60.16
⇔ b = [tex]\sqrt{60.16}[/tex] = 7.76
