Why did the filipinos rebel against american intervention?

Filipinos were already fighting for Independence when the Americans suddenly arrived.  What angered them was the fact that they were not including during the Negotiations between the Americans and the Spanish. It was their freedom that was at stake and they were being left out.  Then they found out that they were now under American rule and this led to war between the Philippines and the Americans.

answer: this problem has only trivial solutions, with all points on the same line. x=5 or x=7/5.

step-by-step explanation:

there are three triangles, and three unknowns: x, y=length of middle segment, and z=cos(angles marked with red arc).

we need

and law of cosines,

the three equations are

see attached image for solution.