In Delta ABC,2R^2 sin A sin B sin C = | vedclass

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

Question

(C) We know that by the Sine Rule,$\frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c} = \frac{1}{2R}$.Therefore,$\sin A = \frac{a}{2R}$,$\sin B =

Vedclass · Accepted Answer

$\Delta$

Vedclass · Answer

(C) We know that by the Sine Rule,$\frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c} = \frac{1}{2R}$.Therefore,$\sin A = \frac{a}{2R}$,$\sin B = \frac{b}{2R}$,and $\sin C = \frac{c}{2R}$.Substituting these into the expression:$2R^2 \sin A \sin B \sin C = 2R^2 \left( \frac{a}{2R} \right) \left( \frac{b}{2R} \right) \left( \frac{c}{2R} \right)$$= 2R^2 \left( \frac{abc}{8R^3} \right)$$= \frac{abc}{4R}$.Since the area of a triangle $\Delta = \frac{abc}{4R}$,the expression equals $\Delta$.

In $\Delta ABC$,$2R^2 \sin A \sin B \sin C = $

Similar Questions

If the angles of a triangle are in the ratio $4:1:1$,then the ratio of the longest side to its perimeter is

In a triangle,the sum of lengths of two sides is $x$ and the product of the lengths of the same two sides is $y$. If $x^2 - c^2 = y$,where $c$ is the length of the third side of the triangle,then the circumradius of the triangle is

In triangle $ABC$, $a=2$, $b=3$ and $\sin A=\frac{2}{3}$, then $B$ is equal to (in $^{\circ}$)

In a triangle $ABC$,if $r_1=6, r_2=9, r_3=18$,then $\cos A=$

If $H$ is the orthocentre of $\triangle ABC$ and $AH=x, BH=y, CH=z$,then $\frac{abc}{xyz}=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module