Answer:C. 45.9Explanation:
The given diagram is a triangle. In order to get the angle m∠A, we will use the cosine rule as shown below:
[tex]a^2=b^2+c^2-2bc\cos m\angle A[/tex]
Given the following:
a = 13
b = 14
c = 18
Substitute the given parameters into the formula:
[tex]\begin{gathered} 13^2=14^2+18^2-2(14)(18)\cos m\angle A \\ 169=196+324-504\cos m\angle A \\ 169=520-504\cos m\angle A \\ 169-520=-504\cos m\angle A \\ -351=-504\cos m\angle A \\ \cos m\angle A=\frac{-351}{-504} \\ \cos m\angle A=\frac{351}{504} \\ \cos m\angle A=0.6964 \\ m\angle A=\cos ^{-1}0.6964 \\ m\angle A=45.85 \\ m\angle A\approx45.9^0 \end{gathered}[/tex]
This shows that option C is correct.
