Finding Triangle's Angle

Question

Find the value of $x$ if the area is $42\;\mathrm{cm}^2$.

The triangle is not right angled or an isosceles.

$X$ is the angle in the bottom left corner of the triangle that I need to find.

The left side of the triangle is $7\;\mathrm{cm}$ in length and the bottom length is $13\;\mathrm{cm}$.

I know that I have to use Heron's formula to work this out but to do this, I need to first find the semi perimeter. However, I can't find the semi perimeter because the right side length is not given, but instead the whole area of the triangle is given ($42\;\mathrm{cm}^2$). I'm really confused on how I should work this whole question out.

Answer 1

You can simply use the relation Area = Base * height / 2 and sin(x).

Please see:

1. find h using 42 = 13 * h / 2
2. substitute h into sin(x) = h / 7

Hope this help!