Cosine Rule

Q. In $\Delta ABC,$ if $AB=10,BC=8,CA=12$ and a point $D$ is taken on $AB$ such that $AD:DB$ is $3:2,$ then the length of $CD$ is

1. $\sqrt{72}$
2. $\sqrt{36}$
3. $\sqrt{24}$
4. $\sqrt{84}$

Q. In a $\Delta ABC,a(bcosC-ccosB)$ is equal to -

1. b + c
2. b - c
3. $b^2-c^2$
4. $b^2+c^2$

Q.

If in a triangle ABC, $\angle C={60}^o,$ then $\frac{1}{a+c}+\frac{1}{b+c}=$
[IIT 1975]

1. $\frac{1}{a+b+c}$

2. $\frac{2}{a+b+c}$

3. $\frac{3}{a+b+c}$

4. None of these

Q. In a $△$ ABC, if $c^2+a^2-b^2=ac,$ then $\angle B=$
[MP PET 1983, 89, 90]

1. $\frac{\pi }{4}$
2. $\frac{\pi }{3}$
3. None of these
4. $\frac{\pi }{6}$

Q.

In $△$ ABC, if 2(bc cos A + ca cos B + ab cos C) =

1. None of these

2. 0

3. a+b+c

4. $a^2+b^2+c^2$

Q.

In $△$ ABC, if cot A, cot B, cot C be in A. P. then $a^2,b^2,c^2$ are in

1. G.P.

2. H.P.

3. A.P.

4. None of these

Q.

In $△$ ABC, if (a+b+c)(a-b+c)=3ac, then
[AMU 1996]

1. $\angle B={60}^o$

2. $\angle B={30}^o$

3. $\angle C={60}^o$

4. $\angle A+\angle C={90}^o$

Q.

If the sides of a triangle are in the ratio $2:\sqrt{6}:(\sqrt{3}+1)$, then the largest angle of the triangle will be

1. ${120}^{\circ }$

2. ${60}^{\circ }$

3. ${90}^{\circ }$

4. ${75}^{\circ }$

Q.

In $\Delta ABC,ifa=3,b=4,c=5,thensin2B=$

1. $\frac{3}{20}$

2. $\frac{1}{50}$

3. $\frac{4}{5}$

4. $\frac{24}{25}$

Q.

In a $\Delta ABC,if\angle C={30}^{\circ },a=47cmandb=94cm$, then the triangle is

1. Right angled

2. Obtuse angled

3. Right angled isosceles

4. Isosceles