Final answer:
By using the ratio obtained from the similar triangles formed by the building and its shadow and the tree and its shadow, the height of the tree is calculated to be 22.5 meters tall.
Step-by-step explanation:
To find the height of the tree, we can use the concept of similar triangles. The building and its shadow create a right triangle, as does the tree and its shadow. With the given information, the ratio of the height of the building to the length of its shadow is 15m/6m. We can assume that the tree and its shadow will have the same ratio since the angles to the sun are the same.
To find the height of the tree (let's call it t), we set up the proportion:
15m/6m = t/9m
By cross-multiplying, we get 15m × 9m = 6m × t. This simplifies to 135m = 6m × t. To find t, we divide both sides by 6m:
135m/6m = t
So t = 22.5m.
Therefore, the tree is approximately 22.5 meters tall when rounded to the nearest tenth.