If a=3+1 cm ∠B=30° ∠C=45° then

∠B=30,∠C=45° but A+B+C=180°⇒A+75°=180° ⇒A=105° asinA=csinC⇒3+1sin(105°)=csin45° ⇒3+13+1=1(12)⇒c=2

If a=3+1 cm ∠B=30° ∠C=45° then

∠B=30,∠C=45° but A+B+C=180°⇒A+75°=180° ⇒A=105° asinA=csinC⇒3+1sin(105°)=csin45° ⇒3+13+1=1(12)⇒c=2

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If $a = \sqrt{3} + 1$ cm $∠ B = 30 °$ $∠ C = 45 °$ then

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\frac{1}{\sqrt{2}}

\frac{\sqrt{3}}{2}

\frac{1}{2}

answer is D.

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Detailed Solution

∠ B = 30, ∠ C = 45 °

but

A + B + C = 180 ° \Rightarrow A + 75 ° = 180 °

$\Rightarrow A = 105 °$

$\frac{a}{\sin A} = \frac{c}{\sin C} \Rightarrow \frac{\sqrt{3} + 1}{\sin (105 °)} = \frac{c}{\sin 45 °}$

$\Rightarrow \frac{\sqrt{3} + 1}{\sqrt{3} + 1} = \frac{1}{(\frac{1}{\sqrt{2}})} \Rightarrow c = 2$

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If a=3+1 cm ∠B=30° ∠C=45° then

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If $a = \sqrt{3} + 1$ cm $∠ B = 30 °$ $∠ C = 45 °$ then