In angle ABC side AB=210cm ,BC=180cm angle B=54° . Find the length of side AC?

Answer 1

Using the law of sines, we have:

AC/sin(B) = BC/sin(A)

AC/sin(54°) = 180cm / sin(A)

AC = (180cm / sin(A)) * sin(54°)

To find sin(A), we can use the fact that the sum of angles in a triangle is 180°:

A = 180° - 54° - C

We can also use the fact that the sine of an angle is equal to the sine of its supplementary angle:

sin(A) = sin(180° - 54° - C) = sin(126° - C)

Now, we can substitute this into the equation for AC:

AC = (180cm / sin(126° - C)) * sin(54°)

However, we don't have enough information to find the exact value of side AC. We need the measure of angle C or another side length in order to solve for AC.