Let's denote the height of the tree by h.
We can use the concept of similar triangles to set up an equation relating the height of the tree to Kaj's height and the lengths of the shadows.
In particular, we can consider the triangle formed by Kaj, the tip of her shadow, and the tip of the tree's shadow, as well as the triangle formed by the tree, the base of its shadow, and the tip of its shadow. These two triangles are similar since they share the same angle at the tip of the shadows and their corresponding sides are proportional.
Therefore, we have:
h / 26.15 = (h + 1.55) / 22
where we add Kaj's height to the length of her shadow to get the total height of the similar triangle.
Simplifying this equation, we can cross-multiply and then solve for h:
h = 26.15 * 1.55 / (22 - 26.15)
h ≈ 12.88 meters
Therefore, the height of the tree is approximately 12.88 meters, rounded to the nearest hundredth of a meter.