I need to know but I don’t want to
climb it to find out! There must be an easier way.

Suppose we walk back a measured distance from the tree. We can
determine this distance using a tape measure. Then we can sight
the top and the bottom of the tree and find the angle each makes
with the horizontal. Foresters measure these angles with a device
called a *clinometer*.

### Setting up the problem - translating from words to symbols:

Let’s do this and see what we get. Suppose we walk
away from the tree a distance of 35 meters. We
then sight the bottom of the tree and find it is
20° below eye
level (As we walked back from the tree, we were climbing a hill).
A similar sighting on the top of the tree reveals it is
43° above eye level.

Look at the above diagram. The total height of the tree is
*y*1 *+
y*2.

The horizontal distance from you to the tree after you have moved
back 35 m is *x*.
Using trigonometric formulas,

*y*2 can be found in two steps.

- First find
*x*:
- Then find
*y*2:

By substituting the first equation into the second,

or

The total height is
*y*1 +
*y*2 = 11.97 + 30.67 =
42.64 m