aleidam2022
Answered

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In ΔABC, a = 640 inches, b = 180 inches and ∠C=7°. Find ∠B, to the nearest degree.

Sagot :

let's first find the side "c", Check the picture below.

now, let's use that value with the law of sines.

[tex]\textit{Law of sines} \\\\ \cfrac{sin(\measuredangle A)}{a}=\cfrac{sin(\measuredangle B)}{b}=\cfrac{sin(\measuredangle C)}{c} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{sin(\measuredangle C)}{c}=\cfrac{sin(\measuredangle B)}{b}\implies \cfrac{sin(7^o)}{461.86}=\cfrac{sin(B)}{180}\implies \cfrac{180sin(7^0)}{461.86}=sin(B) \\\\\\ sin^{-1}\left[ \cfrac{180sin(7^0)}{461.86} \right]= \measuredangle B\implies 2.72^o\approx \measuredangle B\implies \stackrel{\textit{rounded up}}{3^o\approx \measuredangle B}[/tex]

View image jdoe0001
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