Answer:
B)
Step-by-step explanation:
Sides a and c and angle C are given. Use this version of the Law of Cosines:
[tex]b^2=a^2+c^2-2ac\cos{C}[/tex]. Put the given values in this formula.
[tex]b^2=49+25-2(7)(5)\cos{90^\circ} \\ b^2=74-70(0) \\ b^2=74 \\ b=\sqrt{74}[/tex]
An approximation for b is 8.6. Now you're down to choices B and C. Find one more angle. You can find angle A or B -- it doesn't matter which. Let's find angle A.
[tex]a^2=b^2+c^2-2bc\cos B \\ 49=74+25-2(\sqrt{74})\cos A \\ 49=99-10\sqrt{74}\cos A \\ -50=-10\sqrt{74}\cos A[/tex]
[tex]\cos A =\frac{5}{\sqrt{74}} \\ A=\cos^{-1}{\frac{5}{\sqrt{74}}}\\[/tex]
[tex]A=54^\circ[/tex]
The answer is choice B.
