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dexteright02
The side b is opposite to the angle B, applying the law of the sines, we have:

[tex] \frac{a}{sinA} = \frac{b}{sinB} [/tex]
[tex] \frac{20}{sin30^0} = \frac{b}{sin45^0} [/tex]
[tex] \frac{20}{ \frac{1}{2} } = \frac{b}{ \frac{ \sqrt{2} }{2} } [/tex]
[tex]20* \frac{ \sqrt{2} }{2} = b* \frac{1}{2} [/tex]
[tex] \frac{20 \sqrt{2} }{2} = \frac{b}{2} [/tex]
[tex]2*b =2*20 \sqrt{2} [/tex]
[tex]2b = 40 \sqrt{2} [/tex]
[tex]b = \frac{40 \sqrt{2} }{2} [/tex]
[tex]\boxed{b = 20 \sqrt{2} }[/tex]

Answer:

b = 20√2

Step-by-step explanation:

Given: ΔABC

           a = 20 , m∠A =  30° and m∠B = 45°

To find: value of b.

We use Sine result, which state that

[tex]\frac{a}{sin\,A}=\frac{b}{sin\,B}[/tex]

Substituting given values we, get

[tex]\frac{20}{sin\,30^{\circ}}=\frac{b}{sin\,45^{\circ}}[/tex]

we know that [tex]sin\,30^{\circ}=\frac{1}{2}\:and\:sin\,45^{\circ}=\frac{1}{\sqrt{2}}[/tex], we get

[tex]\frac{20}{\frac{1}{2}}=\frac{b}{\frac{1}{\sqrt{2}}}[/tex]

[tex]20{\times2}=b\times\sqrt{2}[/tex]

[tex]b\times\sqrt{2}=40[/tex]

[tex]b=\frac{40}{\sqrt{2}}[/tex]

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

Therefore, b = 20√2

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