UNO High School Problem of the Week Competition
Problem 16
A man had always contemplated the size of a tree behind his house. Standing 5 feet away from his 8 foot high fence, he could barely see the top leaves of the tree over the top of the fence. He knew that the tree was 200 feet from the fence. The man was 6 feet tall, so his line of vision is 67 inches from the ground.
Estimate how tall the tree is.
Show your work.
Solution
tree height = TAN of angle of vision * distance to the tree = 104.7 feet tall
First you need to figure out the angle of vision. The angle of the line of vision over the fence, is the same angle of vision of the eye to the tree top. Height of eyes (67 inches), height of fence (8 ft = 96 inches), distance to fence (5 ft = 60 in)
Angle of vision = inverse TAN ( (96 - 67) / 60) = 25.80 degrees
Distance to tree = 5 ft + 200 ft = 2460 inches
Tree height from eye level = TAN (25.80 deg) * 2460 inches = 1189 inches
Tree height estimate = 1189 inches + 67 inches = 104.7 feet