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.
[Math] Finding unknown angles of a rhombus given side length and area
anglequadrilateraltrigonometry
Best Answer
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.