I have two Law Of Sines Problems that I need to Help Solved! Please!!give me a minute to upload the pictures20 points if answer correct
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Answer:From figure AThe value of ∠ B = 75.74° , ∠ C = 70.26° and AB = 27.37 From figure BThe value of ∠ A = 42.8° , ∠ B = 106.2° and AC = 30.04Step-by-step explanation:Given first figure as :AC = 28.2BC = 16.5 ∠ A = 34°Let AB = cFrom law of sines[tex]\dfrac{a}{Sin A}[/tex] = [tex]\dfrac{b}{Sin B}[/tex] = [tex]\dfrac{c}{Sin C}[/tex] Or, [tex]\dfrac{a}{Sin A}[/tex] = [tex]\dfrac{b}{Sin B}[/tex] or, [tex]\dfrac{16.5}{Sin 34}[/tex] = [tex]\dfrac{28.2}{Sin B}[/tex] Or, 29.506 = [tex]\dfrac{28.2}{Sin B}[/tex] Or, Sin B = [tex]\dfrac{28.2}{29.5}[/tex] Or, Sin B = 0.955∴ ∠B = [tex]Sin^{-1}[/tex] 0.955I.e∠ B = 75.74Now, ∠ C = 180° - ( ∠A + ∠B )Or, ∠ C = 180° - ( 34° + 75.74° )Or, ∠ C = 70.26°Now, Again [tex]\dfrac{b}{Sin B}[/tex] = [tex]\dfrac{c}{Sin C}[/tex] so, [tex]\dfrac{28.2}{Sin 75.74}[/tex] = [tex]\dfrac{c}{Sin 70.26}[/tex] Or, [tex]\dfrac{28.2}{0.9691}[/tex] = [tex]\dfrac{c}{0.9412}[/tex] Or, c = 29.09 × 0.9412∴ c = 27.37 I.e AB = 27.37Hence, The value of ∠ B = 75.74° , ∠ C = 70.26° and AB = 27.37 From figure secondGiven as :AB = c= 12BC = a = 16 ∠ C = 31°let AC = bFrom law of sines[tex]\dfrac{a}{Sin A}[/tex] = [tex]\dfrac{b}{Sin B}[/tex] = [tex]\dfrac{c}{Sin C}[/tex] Or, [tex]\dfrac{a}{SinA }[/tex] = [tex]\dfrac{c}{Sin C}[/tex] or, [tex]\dfrac{16}{Sin A}[/tex] = [tex]\dfrac{12}{Sin 31}[/tex] or, [tex]\dfrac{16}{Sin A}[/tex] = [tex]\dfrac{12}{0.51}[/tex] Or, [tex]\dfrac{16}{Sin A}[/tex] = 23.52∴ Sin A = [tex]\dfrac{16}{23.52}[/tex] I.e Sin A = 0.68Or, ∠ A = [tex]Sin^{-1}[/tex] 0.68or, ∠ A = 42.8°Now, ∠ B = 180° - ( 31° + 42.8° )Or, ∠ B = 106.2°Now, [tex]\dfrac{b}{Sin B}[/tex] = [tex]\dfrac{c}{Sin C}[/tex] or, [tex]\dfrac{b}{Sin 106.2}[/tex] = [tex]\dfrac{16}{Sin 31}[/tex] Or, [tex]\dfrac{b}{0.96}[/tex] = [tex]\dfrac{16}{0.51}[/tex] or, b = 31.3×0.96∴ b = 30.04Hence The value of ∠ A = 42.8° , ∠ B = 106.2° and AC = 30.04Answer