Step 1: Understand that the problem involves a right triangle formed by the tree, its shadow, and the line from the top of the tree to the tip of the shadow.
Step 2: Identify the components of the triangle: the height of the tree is the opposite side, the shadow is the adjacent side, and the angle of elevation of the sun is 30 degrees.
Step 3: Recall the trigonometric function tangent (tan), which relates the opposite side to the adjacent side in a right triangle: tan(angle) = opposite/adjacent.
Step 4: Rearrange the formula to find the height of the tree: height = shadow * tan(angle).
Step 5: Substitute the values into the formula: height = 10 meters * tan(30 degrees).
Step 6: Calculate tan(30 degrees), which is equal to √3/3 or approximately 0.577.
Step 7: Multiply the shadow length by the tangent value: height = 10 * (√3/3) = 10 * 0.577 = 5.77 meters.
Step 8: Note that the short solution provided in the question is incorrect; the correct height of the tree is approximately 5.77 meters.
