Given triangle ABC with sides a,b,c, show that the area of the triangle is given by A=(a^2 sinB sinC)/(2sin(B+C))

Question

This is part of the equivalent trigonometric expressions.

Answer 1

A = a^2sinBCosC/2sin(B+C)

= a^2(b/a)(c/a)/2sin90

= a^2)(bc/a^2)/2

= bc/2 = half base times height = area of a triangle

sin(B+C) = sin(180-A) = sin(180-90)=sin90 = 1

sinB = b/a = opposite side over hypotenuse

CosC = c/a = adjacent side over hypotenuse