Question

In triangle ABC if one side 'c' and two angles a and b are given then the area is ?

Answer 1

Answer:

∆ = (1/2) ab sin(c)

When the angle c is included between sides a and b.

P.S. I think the question is the otherwise.

Answer 2

Answer:

$\frac{x^2sinAsinB}{2sinC}$

Step-by-step explanation:

let’s say you know side C has length  x  and you know two of the three angles of the triangle — of course, since the sum of the measure of the three angles is 180 degrees, you know all three angles.

First, by the law of sines, you can determine the length of either one of the sides — let’s say side B, whose length  y  will be given by:$\frac{y}{sinB} =\frac{x}{sinC}$

$Or, y=\frac{x*sinB}{sinC} \\So,finally\\Area=\frac{1}{2}xy*sinA=\frac{x^2sinAsinB}{2sinC}$