Question

Geometry: Gabriella is 1.25 meters tall. At 3 p.m., she measures the length of a tree's shadow to be 15.45 meters. She stands 10.2 meters away from the tree, so that the tip of her shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter. (There is no image provided)

Answer 1

Let's try to sketch the problem.

From the diagram,

|AC| = 15.45 m, |AB| = 10.2 m |EB| = 1.25 while |DC|=h

Using the idea of similar triangles,

`\begin{gathered} (EB)/(AB)=(DC)/(AC) \\ \\ (1.25)/(5.25)=(h)/(15.45) \\ \\ \Rightarrow h=(15.45*1.25)/(10.2)\approx1.89m(\text{Nearest hundredth)} \end{gathered}`

Therefore, the height of the tree is 1.89m