Question

A certain rock rises almost straight upward from the valley floor. from one​ point, the angle of elevation of the top of the rock is 22.6 degrees. from a point 191 m closer to the​ rock, the angle of elevation of the top of the rock is 39.9 degrees. how high is the​ rock?

Answer 1

Seeing the image attached, we can then get tan (22.6) = opposite/adjacent = opposite/191, and tan(22.6)*191=opposite side length, which is the hypotenuse of the right triangle. sin (39.9) is then opposite/hypotenuse, and we want to find the opposite (the height). To get that, we have
sin(39.9)=opposite/tan(22.6)*191 and then sin(39.9)*tan(22.6)*191=height