Question

Large tree casts a shadow of 90m. At the same time, a 9m high fence, standing vertically, casts a shadow of 15m. Find h, the height of the tree.

Answer 1

Using the concept of similar triangles, the height of the tree is calculated to be 54 meters based on the proportion of the fence's height to its shadow length and the tree's shadow length.

Step-by-step explanation:

To find the height of the tree, h, we can use the concept of similar triangles since the tree and the fence cast shadows at the same time. Given that a 9m high fence casts a 15m shadow, we can set up a proportion with the tree's height and its 90m shadow.

The proportion based on similar triangles would be:

• Fence height / Fence shadow length = Tree height / Tree shadow length
• 9m / 15m = h / 90m

To find the height of the tree, h, we solve the proportion:

• 9m / 15m = h / 90m
• h = (90m × 9m) / 15m
• h = 54m

Therefore, the height of the tree is 54 meters.