A: In ΔABC if A:B:C=5:1:6 then a:b:c=3+1:22:3−1 R: In ΔABC, asinA=bsinB=csinC

A:B:C=5:1:6A=55+1+6×180∘=75B=15∘; C=90∘∴ a:b:c=sinA:sinB:sinC =3+122:3−122:1 =3+1:3−1:22 A is false R: sine rule → True

A: In ΔABC if A:B:C=5:1:6 then a:b:c=3+1:22:3−1 R: In ΔABC, asinA=bsinB=csinC

A:B:C=5:1:6A=55+1+6×180∘=75B=15∘; C=90∘∴ a:b:c=sinA:sinB:sinC =3+122:3−122:1 =3+1:3−1:22 A is false R: sine rule → True

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A: In $Δ A B C$ if $A : B : C = 5 : 1 : 6$ then $a : b : c = \sqrt{3} + 1 : 2 \sqrt{2} : \sqrt{3} - 1$
R: In $Δ A B C, \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$

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A is true, R is true and R is correct explanation of A

A is true, R is true and R is not correct explanation of A

A is true, R is false

A is false, R is true

answer is D.

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Detailed Solution

$\begin{array}{l} A : B : C = 5 : 1 : 6 \\ A = \frac{5}{5 + 1 + 6} \times 180^{\circ} = 75 \\ B = 15^{\circ}; C = 90^{\circ} \\ ∴ a : b : c = \sin A : \sin B : \sin C \\ = \frac{\sqrt{3} + 1}{2 \sqrt{2}} : \frac{\sqrt{3} - 1}{2 \sqrt{2}} : 1 \\ = \sqrt{3} + 1 : \sqrt{3} - 1 : 2 \sqrt{2} \end{array} A i s f a l s e R : \sin e r u l e \to T r u e$