Finding unknown angles of a rhombus given side length and area

Question

Given that the area of a rhombus is $40 \text{cm}^2$ and that each side has a length of $15 \text{cm}$, find the angles of the rhombus.

It's from a 8th-grade school math textbook.

Answer 1

Since the area of a triangle is given by $\frac{sin(A)bc}{2}$, and there are two isosceles triangles which make up the rhombus (imagine drawing a diagonal, splitting the rhombus in two) we know that $sin(A)bc=area$. (by applying the sine rule to each of the smaller triangles).

Substituting area = 40, b=c=15 yields $sin(A)=\frac{8}{45}$ so $A=10.24$ or $169.76$ degrees.

Answer 2

Hint:

$h\cdot 15=40\implies h=\dfrac{40}{15}$

Now you know the height of Rhombus. Carry it from here...