Question

The figure shows a person estimating the height of a tree by looking at thetop of the tree with a mirror. Assuming that both the person and the tree formright angles with the ground, which of the following proportions can be usedto estimate the height of the tree?6 ft3 ft7 fthft

Answer 1

SOLUTIONS

Using the rule of SOHCAHTOA:

The height of the tree compared to the height of the boy is tangent:

$tan\theta=\frac{opp}{adj}$

For the small triangle:

$tan\theta=\frac{6}{3}.........(1)$

For the Big triangle:

$tan\theta=\frac{h}{7}..........(11)$

Equating (1) and (11

$\begin{gathered} \frac{6}{3}=\frac{h}{7} \\ \frac{6}{h}=\frac{3}{7} \end{gathered}$

Hence the correct answer = Option A