A large elm tree died after it was struck by lightning. The property owner thinks he can remove it himself, but is concerned that it will fall on his greenhouse. He takes several measurements before attempting to cut it down. At 3 PM he measures the shadow of the tree and finds it to be 15 feet long. He also determines that the tree is 27 feet from the greenhouse. What else must he know to be able to determine the height of the tree?

To determine the height of the tree, the property owner would need to know the length of the shadow cast by an object of a known height at the same time and under the same conditions. Without this information, it is not possible to accurately determine the height of the tree.

To determine the height of the tree, the property owner needs to know the length of his own shadow at the same time of day. With that information, he can use the concept of similar triangles to solve for the height of the tree.

Here's how he can determine the height of the tree:

1. Choose a time of day when the sun is at a known altitude. This will ensure that the shadows cast by objects are directly proportional to their respective heights.

2. Measure the length of the property owner's shadow at the chosen time of day. Let's say his shadow is 10 feet long.

3. Set up a proportion using the lengths of the shadows and the distances between the objects. In this case, the property owner can set up the following proportion:

Height of the tree / Length of the tree's shadow = Height of the property owner / Length of the property owner's shadow

Let's denote the height of the tree as "h." The proportion becomes:

h / 15 feet = Height of the property owner / 10 feet

4. Now, solve the proportion for "h." Cross-multiply and divide to isolate "h":

h = (Height of the property owner / 10 feet) * 15 feet

5. Plug in the appropriate values to find the height of the tree. For example, if the property owner is 6 feet tall, the calculation would be:

h = (6 feet / 10 feet) * 15 feet

h = 0.6 * 15 feet

h ≈ 9 feet

Therefore, the height of the tree is approximately 9 feet.

assuming sunset at 6 pm, the angle of elevation of the sun at 3 pm is 45°, so the shadow is as long as the tree's height.