I am a geometry teacher trying to solve a problem. Our textbook only gives us the answer and I am the only HS math teacher at the school. One of my students figured it out, but I cannot understand his solution and I think he assumed something he cannot assume. The question is:
Find the measure of the obtuse angle of a rhombus given that it has side lengths of 2in and a height of 1in.
My student assumed that the height is also equal to a diagonal, but from my knowledge you cannot do that.
but it is $$\sin(\alpha)=\frac{h}{a}$$ and the other angle is $$180^{\circ}-\alpha$$ whre $a$ is the side length of the given rhombus and $h$ the hight. so $$\alpha=\frac{\pi}{6}$$ and the searched angle is $$\frac{5\pi}{6}$$