Final answer:
To find the height of the tree, we can use the concept of similar triangles. The distance from Mary to the tree is the base of the smaller triangle, and the distance from Mary to the top of the ladder is the hypotenuse of the larger triangle. The height of the tree can be calculated using these measurements and the given options.
Step-by-step explanation:
To find the height of the tree, we can use the concept of similar triangles. The distance from Mary to the tree (30m) is the base of the smaller triangle, and the distance from Mary to the top of the ladder (35.6m) is the hypotenuse of the larger triangle. The height of the tree is the corresponding side of the larger triangle. We can set up a proportion:
(height of tree)/(30m) = (35.6m)/(hypotenuse of larger triangle)
We can cross multiply and solve for the height of the tree:
height of tree = (35.6m * 30m) / (hypotenuse of larger triangle)
Using the given options, we can calculate the height of the tree:
a) 22.0m: (35.6m * 30m) / 22.0m = 154.91m
b) 25.4m: (35.6m * 30m) / 25.4m = 132.68m
c) 28.8m: (35.6m * 30m) / 28.8m = 147.22m
d) 30.5m: (35.6m * 30m) / 30.5m = 111.50m
Based on the calculations, the height of the tree is closest to 150m. Therefore, the correct answer is option a) 22.0m.