Question

What is the height of the tree nearest tenth of a foot?

Answer 1

Explanation

Let's picture the situation of the exercise:

We're looking for the value of the height of the tree; namely, for the value of h in the drawing. Laying down the drawing, we get

Since both triangles are similar, we can apply the Geometric Mean theorem, which says that

$(9.2)^2=4.2\cdot x.$

Solving this equation for x, we get

$\begin{gathered} (9.2)^2=4.2\cdot x, \\ 84.64=4.2\cdot x, \\ x=\frac{84.64}{4.2}, \\ x\approx20.15 \end{gathered}$

However, note that

$h=4.2+x\approx4.2+20.152=24.35.$

Now, since the second decimal place of our approximation of h is exactly 5, the rounding rule says that we must eliminate 5 and add one to the tenths, to get 24.2.

Answer

The height of the tree is (approximately) 24.2 ft.