If in a triangle ABC,s(s-a) = (s-b)(s-c),then | vedclass

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

Question

(C) Given,$s(s-a) = (s-b)(s-c)$.We know that $\sin \frac{A}{2} = \sqrt{\frac{(s-b)(s-c)}{bc}}$ and $\cos \frac{A}{2} = \sqrt{\frac{s(s-a)}{bc}}$.Squar

Vedclass · Accepted Answer

$\angle A = \frac{\pi}{2}$

Vedclass · Answer

(C) Given,$s(s-a) = (s-b)(s-c)$.We know that $\sin \frac{A}{2} = \sqrt{\frac{(s-b)(s-c)}{bc}}$ and $\cos \frac{A}{2} = \sqrt{\frac{s(s-a)}{bc}}$.Squaring both,we get $\sin^2 \frac{A}{2} = \frac{(s-b)(s-c)}{bc}$ and $\cos^2 \frac{A}{2} = \frac{s(s-a)}{bc}$.Since $s(s-a) = (s-b)(s-c)$,it follows that $\sin^2 \frac{A}{2} = \cos^2 \frac{A}{2}$.Dividing by $\cos^2 \frac{A}{2}$,we get $	an^2 \frac{A}{2} = 1$.Since $\frac{A}{2}$ is an angle of a triangle,$\frac{A}{2} = \frac{\pi}{4}$,which implies $A = \frac{\pi}{2}$.

If in a $\triangle ABC$,$s(s-a) = (s-b)(s-c)$,then

Similar Questions

In $\triangle ABC$,$a^2 \sin 2B + b^2 \sin 2A =$

The ratio of the sides of triangle $ABC$ is $1:\sqrt{3}:2$. The ratio of angles $A:B:C$ is

If in a triangle $ABC$,$a, b, c$ are sides and angle $A$ is given,and $c \sin A < a < c$,and $b_1$ and $b_2$ are two possible values of $b$,then:

If the sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one,then the area (in sq. units) of that triangle is

In a $\triangle ABC$, $a^2 \sin 2C + c^2 \sin 2A$ is equal to (in $\Delta$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module