If the angles of a triangle ABC are in A.P.,t | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given that the angles $A, B, C$ are in $A.P.$,we have $A + C = 2B$. Since $A + B + C = 180^\circ$,substituting $A + C = 2B$ gives $3B = 180^\circ$

Vedclass · Accepted Answer

$b^2 = a^2 + c^2 - ac$

Vedclass · Answer

(B) Given that the angles $A, B, C$ are in $A.P.$,we have $A + C = 2B$. Since $A + B + C = 180^\circ$,substituting $A + C = 2B$ gives $3B = 180^\circ$,so $B = 60^\circ$. Using the cosine rule,$\cos B = \frac{a^2 + c^2 - b^2}{2ac}$. Substituting $B = 60^\circ$,we get $\cos 60^\circ = \frac{1}{2} = \frac{a^2 + c^2 - b^2}{2ac}$. This simplifies to $ac = a^2 + c^2 - b^2$,which rearranges to $b^2 = a^2 + c^2 - ac$.

If the angles of a triangle $ABC$ are in $A.P.$,then

Similar Questions

If the angles of a triangle $ABC$ are in the ratio $1: 2: 3$,then the corresponding sides are in the ratio

In a triangle $ABC$,with usual notations,if $3b = a + c$,then $\cot \frac{A}{2} \cdot \cot \frac{C}{2} = $

In any triangle $ABC$,$\sin \frac{A}{2} \leq$

The smallest angle of the $\Delta ABC$,when $a = 7, b = 4\sqrt{3}$ and $c = \sqrt{13}$,is .....$^o$

In a triangle $ABC$,if $b + c = 2a$ and $\angle A = 60^\circ$,then $\Delta ABC$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module