### Brain Teasers

# Old Oak Tree

Homer had always contemplated the size of the old oak tree in the field behind his house. Standing 5 feet away from the 8 foot high fence in the back of the yard, he could just 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. Homer was 6 feet tall, making his line of vision, 67 inches from the ground.

Estimate how tall the old oak tree is.

Estimate how tall the old oak tree is.

### Hint

TAN A = opposite / adjacent, remember trigonometry### Answer

tree height = TAN of angle of vision * distance to the tree = 104.7 feet tallFirst 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

This is an old lumberjack method of estimating a tree height. With pure math the height of 104.7 feet is correct. With the measurement capabilities available to any lumberjack (or any average Homer) precise measurements are not possible. Thus the need to clarify these calculations as estimates.

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