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Solve the triangle for which ∠ A = 30 ∘ , ∠ B = 45 ∘ , and a = 20 . Round to the nearest whole number. Do not use a decimal point or spaces in your answer or it will be marked incorrect. b = ∘

Respuesta :

Answer:

[tex]b=20\sqrt{2}[/tex] units

Step-by-step explanation:

Recall the Law of Sines

[tex]\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}[/tex]

Solve for side "b" given ∠A, ∠B, and side "a"

[tex]\frac{sinA}{a}=\frac{sinB}{b}\\ \\\frac{sin(30^\circ)}{20}=\frac{sin(45^\circ)}{b}\\ \\ bsin(30^\circ)=20sin(45^\circ)\\\\b(0.5)=20(\frac{\sqrt{2}}{2})\\ \\0.5b=10\sqrt{2}\\\\b=20\sqrt{2}[/tex]

Therefore, [tex]b=20\sqrt{2}[/tex] units

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