Here is Eric's presentation about how he used triangle trig to measure the height of a tree in his front yard.

1. How to Measure the Height of
A Tree using Trigonometry
By Eric Sweet

2. 1) Collect your equipment
What you’ll need:
1. Handheld laser
2. Print-out of 180-degree semicircle
3. Level
4. Tape
5. Ruler
6. Tape measure

3. • Tape the semicircle to the front of the
ruler
• Tape the side of the ruler down to the
top of the level

4. 2) Find the tree
The height of this tree
in my front yard is WAY
too tall to be measured.
But we can use
trigonometry and the
Law of Sines to find the
height mathematically!
As you will see, the following
data collection is best done at
night!

5. 3) Set up distance (D)
When it is dark outside,
pick a spot far enough
away from the tree so that
you can see the top of the
canopy. The angle of
elevation from eye
height to the top must
be an acute angle!
Measure out distance from
the spot to the base of the
tree with a tape measure.
My D is 82 feet (see next slide).

6. 4) Find your eye level height
(HE)
Standing up straight, find the height of your
eye level. Record as HE. This step will be very
important later on! My eye level is 62.5
inches.
HE -------->
D

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

8. Place the laser at the bottom center of the
semicircle. Look up the laser at the top of the
tree. The laser should illuminate your line of
sight (using a green, 10mW laser, the beam can
be clearly seen in the air at night).

10. -

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

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