Napier’s Analogy

Q. In a triangle ABC, a = 6, b = 3 and $\tan \left(\frac{A-B}{2}\right)=\frac{1}{3}$. Area of triangle ABC = sq. units.

1. 4
2. 16
3. 3
4. 9

Q. If $a,b,c$ are the sides opposite to angles $A,B,C$ of a triangle $ABC,$ respectively and $\angle A=\frac{\pi }{3},b:c=\sqrt{3}+1:2,$ then the value of $\angle B-\angle C$ is

1. $\frac{\pi }{2}$
2. $\frac{\pi }{12}$
3. $\frac{\pi }{6}$
4. $\frac{\pi }{4}$

Q. If $a,b,c$ are the sides opposite to angles $A,B,C$ of a triangle $ABC,$ respectively and $\angle A=\frac{\pi }{3},b:c=\sqrt{3}+1:2,$ then the value of $\angle B-\angle C$ is

1. $\frac{\pi }{2}$
2. $\frac{\pi }{6}$
3. $\frac{\pi }{12}$
4. $\frac{\pi }{4}$

Q. If in a triangle $ABC,a=5,b=4$ and $\cos (A-B)=\frac{31}{32}$. then the third side $c$ is equal to

1. 3
2. 6
3. 7
4. 9

Q. If in a triangle a = $\sqrt{3}+1,b=\sqrt{3}-1,C={60}^{\circ }$ then the value of A is ?

1. ${75}^{\circ }$
2. ${90}^{\circ }$
3. ${105}^{\circ }$
4. ${120}^{\circ }$