How to Measure the Height ofA Tree using Trigonometry

By Eric Sweet

1) Collect your equipmentWhat you’ll need:1.Handheld laser2.Print-out of 180-degree semicircle3.Level4.Tape5.Ruler6.Tape measure

• Tape the semicircle to the front of theruler

• Tape the side of the ruler down to thetop of the level

2) Find the tree

The height of this treein my front yard is WAYtoo tall to be measured.But we can usetrigonometry and theLaw of Sines to find theheight mathematically!

As you will see, the followingdata collection is best done atnight!

3) Set up distance (D)When it is dark outside,pick a spot far enoughaway from the tree so thatyou can see the top of thecanopy. The angle ofelevation from eyeheight to the top mustbe an acute angle!

Measure out distance fromthe spot to the base of thetree with a tape measure.My D is 82 feet (see next slide).

4) Find your eye level height(HE)

Standing up straight, find the height of youreye level. Record as HE. This step will be veryimportant later on! My eye level is 62.5inches.

HE --------> D

5) Find angle of elevationStanding straight and looking directly at the tree,hold the level and semicircle to the left of your lefteye at eye level, level with the ground.

Place the laser at the bottom center of thesemicircle. Look up the laser at the top of thetree. The laser should illuminate your line ofsight (using a green, 10mW laser, the beam canbe clearly seen in the air at night).

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Now try to determine the angle of elevation asshown by the laser beam on the semicircle.This angle is about 55 degrees.

55 degrees

Using the D (82 ft), HE (62.5 in), and the angle of elevation (55degrees), we can make 2 right triangles and use Law of Sines tofind the height of the tree (HT); for my tree it is about 122 feet tall!

D

degrees

HT

HE