Solve each of the following triangles, i. e. find all missing side and angle measures. There may be two groups of answers for some exercises. Round answers to the nearest hundredth. If no such triangle exists, state "No such triangle exists."

What are the measures of angles a, b, and c? show your work and explain your answers. 25 points

Two poles, ab and ed, are fixed to the ground with the of ropes ac and ec, as shown: what is the approximate distance, in feet, between the two poles? 6.93 feet 8.66 feet 12.32 feet 15.59 feet

Acone is placed inside a cylinder. the cone has half the radius of the cylinder, but the height of each figure is the same. the cone is tilted at an angle so its peak touches the edge of the cylinder’s base. what is the volume of the space remaining in the cylinder after the cone is placed inside it?