Question

How many meters tall is the tree?

Nate heard stories about the massive Sierra redwoods in California and looked forward to seeing one of these trees for himself. On his first actual encounter with one of the trees, Nate wants to know just how tall the tree is. He places a mirror on the ground and experiments several times until he determines the correct distance from the base of the tree as well as the correct angle of incidence that allows him to see the top of the tree.

Answer 1

95 meters

Explanation:

Given the dimensions of the triangles shown in the figure, you want the height of the tree.

Similar triangles

The ratio of the height of the triangle to the base is the same for both triangles shown. That means ...

1.9/0.75 = x/(38.25 -0.75)

where x represents the height of the tree.

Multiplying by (38.25 -0.75), we have ...

`x=((38.25-0.75)\cdot1.9)/(0.75)=1.9\left((38.25)/(0.75)-1\right)=95`

The height of the tree is 95 meters.