Question

Someone please help me with this question i really need help

Answer 1

Answer:

b = 7.76

Step-by-step explanation:

ABC is a triangle. In a triangle, we have the formula as following:

+) Cosine ∠An angle = $\frac{Adjacent side a^{2} + Adjacent side b^{2} - Opposite side^{2} }{ 2 * Adejacent side a* Adejacent side b}$

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 = $\frac{AB^{2}+BC^{2}-AC^{2} }{2ABBC}$

⇔ Cosine 40° = $\frac{10^{2}+12^{2} -b^{2} }{2*10*12}$

⇔ 0.766 = $\frac{244 - b^{2} }{240}$

⇔ 0.766 x 240 = 244- b^2

⇔ 183.84 = 244 -b^2

⇔ b^2 = 244 - 183.84 = 60.16

⇔ b = $\sqrt{60.16}$ = 7.76