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?

Question

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?

Steve · Answer

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.