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Given ΔABC with m∠B = 62°, a = 14, and c = 16, what is the measure of A? Use the law of cosinus.

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Given data,


\begin{gathered} \angle B=62 \\ a=14\text{ } \\ c=16 \end{gathered}

Use the law of cosines.


\begin{gathered} b^2=a^2+c^2-2acCos(B) \\ b^2=14^2+16^2-(2*14*16* Cos(62)) \\ b^2=196+256-210.32 \\ b^2=241.68 \end{gathered}

Thus, the value of b is


b=15.54

The cosines formula for angle A isThus, angle A will be


a^2=b^2+c^2-2bcCos(A)


\begin{gathered} A=cos^(-1)\lbrack(b^2+c^2-a^2)/(2bc)\rbrack \\ A=\cos ^(-1)\lbrack(15.54^2+16^2-14^2)/(2*15.54*16)\rbrack \\ A=52.67 \end{gathered}

Therefore, angle A is 52.67 degrees.

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