Measuring a tree with a mirror

To find the height of a tree, Mei places a small flat mirror on level ground \(12.0\) m from the foot of the tree. She stands \(2.0\) m from the mirror, on the far side from the tree, and just sees the top of the tree in the mirror. Her eyes are \(1.5\) m above the ground. At the mirror, the angle between the ground and the line of sight from her eye equals the angle between the ground and the line from the top of the tree.

1. Explain why the two triangles formed are similar, and find the height of the tree.[3]
2. State two assumptions made in this method.[2]
3. Each of the three measurements \(1.5\) m, \(2.0\) m and \(12.0\) m is correct to the nearest \(0.1\) m. Find the greatest possible height of the tree consistent with these measurements.[3]