Question

In triangle abc, ac=12, the measure of angle a = 30\deg, and the measure of angle b = 45\deg. find the area of this triangle.

Answer 1

First we have to find the missing angle. And we know that sum of the measurement of angles of a triangle is 180.

So we will get

$C = 180-30-45 = 105 degree$

Now we use sine law, which is

$\frac{sin \ A}{BC} = \frac{sin \ B }{AC}$

Substituting the values, we will get

$\frac{sin 30}{BC} = \frac{sin 45}{12}$

$BC = \frac{12 sin 30}{sin 45} = 6 \sqrt2$

The formula of area of triangle, for the given triangle is

$Area= \frac{1}{2}AC*BC sinC$

$Area = \frac{1}{2}*12*6 \sqrt 2 sin(105)= 49.2 \ square \ units$